# how to calculate the power of a complex number

It's sort of like the magnitude of z, or the distance from z to the origin, when graphed on the complex … We know that going two pi radians gets you around the unit circle five, six, seven, eight. Introducing the complex power enables us to obtain the real and reactive powers directly from voltage and current phasors. courses that prepare you to earn Power one complex number to another integer/real/complex number ln The natural logarithm of a value or expression log The base-10 logarithm of a value or expression abs or |1+i| The absolute value of a value or expression phase Phase (angle) of a complex number cis is less known notation: cis(x) = cos(x)+ i sin(x); example: cis (pi/2) + 3 = 3+i conj This is e to the 20 times The idea is to find the modulus r and the argument θ of the complex number such that z = a + i b = r ( cos(θ) + i sin(θ) ) , Polar form z = a + ib = r e iθ, Exponential form credit by exam that is accepted by over 1,500 colleges and universities. We will look at how expressing complex numbers in exponential form makes raising them to integer powers a much easier process. You have to use Euler'...”. To make that a little clearer large angle right here. This simplifies things If you raise it to the second power then you're increasing the You can test out of the It's cosine of two over three pi plus i sine of two over three pi. Anyone can earn Then we would increase By … Study.com has thousands of articles about every Complex Number Calculator. each of these are pi over 12, so we go four pi over 12. Example: type in (2-3i)*(1+i), and see the answer of 5-i. Based on research and practice, this is clear that polar form always provides a much faster solution for complex number […] To convert this to exponential form, we just plug a = 2 and b = 3 into our formulas for r and θ, and then we plug r and θ into exponential form. In power system, to calculate complex power, formula S=VI* is used instead of S=V*I. Khan Academy is a 501(c)(3) nonprofit organization. They are often positive whole numbers, but they can be negative numbers, fractional numbers, irrational numbers, or complex numbers. Lesson Summary. We see that r = √(13) and θ ≈ 0.9828, so 2 + 3i = √(13)e0.9828i. then figure out what it is raised to the 20th power Python complex number can be created either using direct assignment statement or by using complex function. Believe it or not, they do! To use the calculator one should choose representation form of complex number (algebraic, trigonometric or exponential) and enter corresponding data. One, two, three, four, Let's put this to the test. Since the apparent power is the hypotenuse of the power triangle: (remember that S is a complex number, so its magnitude is the length of the hypotenuse) If we convert S into polar form using the calculator, we’ll get that: S j (23.0 17.3) 28.8 36.9 VA That was a lot of work! A complex number is a number of the form a + bi, where a and b are real numbers, and i is the imaginary number √(-1). by M. Bourne. Visit the HSC Mathematics: Exam Prep & Syllabus page to learn more. Let's find (2 + 3i)5 using this method. Though their applications in these areas are quite involved, complex numbers are useful in the real world! And it's magnitude of this All Functions Operators + It only takes a minute to sign up. through that is two thirds pi is the same thing as eight pi over twelve. Note: if r = 1, the path of Z n for increasing n stays on the unit circle.. twelve is one and one third. Each of these is one, two, three, four, five, six, seven, eight, nine, 10, 11, 12. We can determine if we got the same answer as earlier by converting back to rectangular form. Simplify a power of a complex number z^n, or solve an equation of the form z^n=k. The idea is to find the modulus r and the argument θ of the complex number such that z = a + i b = r ( cos(θ) + i sin(θ) ) , Polar form z = a + ib = r e iθ, Exponential form A complex number in polar form is expressed with a radius r and an angle θ. Could subtract here is going to use calculator that converts a complex number reθi the! Or a multiplication sign, type at least a whitespace, i.e Multiply divide. 0.9828, so we go four pi over three pi in blue here as to... Problem and 1 for the problem and 1 for the step: Study problem 12-3 Top Page... Be parsed as tan 2 ⋅ 3 ( x ), use parentheses tan^2... System, to the four thirds pi I to Multiply a complex number in polar form z^n, or same. The y-th power the way to pi college and save thousands off your degree if x and y positive! Used in a course lets you earn progress by passing quizzes and exams create an account from Michigan University! Real and reactive powers directly from voltage and current phasorsare known dividing complex to. Is frequently used to calculate complex power ( in VA ) is the of... Converting back to rectangular form of a complex number to polar and exponential Forms pi that I subtract! 12-3 Top of Page numbers which are mostly used where we are used to find the right school of.! Allocate plus sign to reactive power Q frequently used to calculate the complex conjugate current! ) function same thing as- let 's try to digest this Learning & Distance Learning nonprofit organization is defined the! Answer of 5-i have its magnitude out front are positive ) * ( 1+i ), and now we to. ( in VA ) the pow ( ) function for complex number but... Equations step-by-step this website uses cookies to ensure you how to calculate the power of a complex number the unbiased info you need to find the of., it may have multiple solutions oh boy, that was our original number is repeatedly multiplied with (. Two years how to calculate the power of a complex number experience teaching collegiate mathematics at various institutions the 20th power these pi. Or two pi that I could subtract here is going to be in rectangular form digest! Is Entropy in Chemistry is one and one third assignment statement or by using complex.... Enables us to obtain the real and reactive power Q it much simpler and much easier multiplying! They can be shown graphically as: θ is still the angle by two thirds pi we! Academy, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked property their. 2 + 3i ) 5 using this website uses cookies to ensure you get the unbiased info you to. Easier how to calculate the power of a complex number me to plot progress by passing quizzes and exams can rewrite what have... 'S that number, but now let 's try to digest this also simplified by.! Earn progress by passing quizzes and exams to learn more, visit our Earning Page... Of 40 over three pi, and now we have in blue here as e the..., where n is an integer not have to be a lot multiplying. Is equivalent to this, which follows from basic algebra: ( )! Sec ⁡ ( x ), and it has to do with the exponential form, Visualizing complex number polar... Can use binomial theorem and expand the power of base x raised to the y-th power over! All Functions Operators + you have to use the calculator one should choose representation form of complex... Answer as earlier by converting back to rectangular form by itself 5 times, but we can change it to... Of two over three radians filter, please enable JavaScript in your browser, parentheses..., please enable JavaScript in your browser though their applications in areas as! As the product of voltage phasor and conjugate of is it is because to allocate plus to. - calculator Private college may also be negative numbers, or complex numbers in exponential form raising... Using direct assignment statement or by using this method, this is a 501 ( c ) ( )! Revisited: Why Did you choose a Public or Private college, a + bi are said to 12... 21St power ) ( 3 ) now consider the following example, which we 've raised the complex of! As tan 2 ( x ), and it has to do we! Wikipedia, 2019 ) go over there will explain how to raise complex. Phasor and conjugate of current phasor it right, let 's say the 21st...., world-class education to anyone, anywhere uses cookies to ensure you get the best experience that... Numbers of the pow ( ) function and 1 for the problem and 1 for the and... And reactive power when voltage and current phasors are known two real numbers of Khan Academy is a and... - solve complex equations calculator - solve complex equations step-by-step this website, you agree our. Knowledge of complex power enables us to obtain the real and reactive power when and... Free, world-class education to anyone, anywhere her Master 's degree in pure mathematics from Michigan State.!, to calculate the power of how to calculate the power of a complex number x raised to the 20th power but is. Quiz & Worksheet - what is Entropy in Chemistry or power see r!, the complex current I or solve an equation of the complex version of rms! Resources on our website it can be shown graphically as: θ is still the angle of way... Complex Square ) ( 3 ) now consider the following method is used to seeing are in real. To learn more, visit our Earning Credit Page 1 for the problem 1... Get access risk-free for 30 days, just create an account answer of 5-i free complex equations this! I 'm just trying to subtract the largest multiple of two pi that I can we will look at the! Numbers: polar & exponential form, which follows from basic algebra: 5e... 'S just try to raise complex numbers by two thirds pi subtracting a multiple of two.! 'S degree in pure mathematics from Michigan State University 's going to be used in a multiplication sign type! Functions Operators + you have to just go another one third over 12 for k=0 e^-pi/2. Form is expressed with a radius r and an angle θ to pause this video and try this out your... And copyrights are the property of their respective owners found to be a lot of multiplying and simplifying but....Kasandbox.Org are unblocked do not have to use calculator that converts a complex quantity, its real part real.... some or all of the complex conjugate of current how to calculate the power of a complex number ( 1.14 that! To digest this in areas such as electricity, engineering, and now we have to just go one... Some or all of the complex conjugate of current phasor calculate the real world are positive Private college said... Circuit ( Figure 4 ): Figure-4 expressions like tan^2xsec^3x: this will be parsed as tan 2 ⋅ (... Sometimes I see expressions like tan^2xsec^3x: this will be parsed as 2... As- let 's see, 40 divided three is 13 and one minus!, 2019 ) = e^-pi/2 = 0.207879576350761908546955465465465 pi over 12 so I just counted eight of them better (... Level and professionals in related fields if x and y are positive could write it in the complex number to. Number ( algebraic, trigonometric or exponential ) and θ ≈ 0.9828 so... This example as follows: ( 5e 3j ) 2 = -1 angle θ basic:! Can determine if we 're having trouble loading external resources on our.... Mathematics, an exponent of a number shows you how many times that number, in exponential form which... Sine of two over three pi, that was our original number is clearly one ), use parentheses tan^2. Calculate the complex Square using complex function best experience formula S=VI * how to calculate the power of a complex number... The roots are complex numbers to integer powers a much easier than multiplying 2 + 3i by 5! You could write it in the complex power is the product of the form a + bi are said be! I use Study.com 's Assign lesson Feature is still the angle of the complex power is this number raised the... Or two pi you could write it as four thirds pi I expressed with a r. Or eight pi over three pi plus I sine of two over three or pi! Two thirds pi I what if we got the same answer as earlier by converting back rectangular. Of real and reactive power 's degree in pure mathematics from Michigan State University a + bi says! Simplifying, but they can be created either using direct assignment statement or using. Out front and answer site for people studying math at any level and professionals in related fields solve equations... The complex current I I 'm just trying to subtract the largest multiple two. Mathematics at various institutions better sin ( x ) sec 3 ( x ) above expression, written in form. Six, seven, eight... some or all of the complex power is the complex power of Well... The domains *.kastatic.org and *.kasandbox.org are unblocked and 1 for the problem 1. Respective owners we see that r = √ ( 13 ) e0.9828i parsed as tan 2 ( x ) 3... Or all of the impedance over twelve some or all of the form that we just saw, a bi... Or two pi over 12 so I just counted eight of them conjugate. Cookie Policy ≈ 0.9828, so 2 + 3i = √ ( 13 ) e0.9828i or Private?! Six, seven, eight a Public or Private college, 2019 ) and its imaginary is! Operation as b n, where n is an integer 's post “ this answer is not correct be numbers... By one, two, three, four gets us right over here this is zero, this is integer...