![]() Because of the fundamental theorem of algebra, you will always have two different square roots for a given number. Square root of complex number (a+bi) is z, if z 2 = (a+bi). The calculator uses the Pythagorean theorem to find this distance. The absolute value or modulus is the distance of the image of a complex number from the origin in the plane. If the denominator is c+d i, to make it without i (or make it real), multiply with conjugate c-d i: ![]() This approach avoids imaginary unit i from the denominator. The division of two complex numbers can be accomplished by multiplying the numerator and denominator by the denominator's complex conjugate. This is equal to use rule: (a+b i)(c+d i) = (ac-bd) + (ad+bc) i To multiply two complex numbers, use distributive law, avoid binomials, and apply i 2 = -1. This is equal to use rule: (a+b i)+(c+d i) = (a-c) + (b-d) i This is equal to use rule: (a+b i)+(c+d i) = (a+c) + (b+d) iĪgain very simple, subtract the real parts and subtract the imaginary parts (with i): Very simple, add up the real parts (without i) and add up the imaginary parts (with i): Many operations are the same as operations with two-dimensional vectors. And use definition i 2 = -1 to simplify complex expressions. We hope that working with the complex number is quite easy because you can work with imaginary unit i as a variable. Complex numbers in the angle notation or phasor ( polar coordinates r, θ) may you write as rLθ where r is magnitude/amplitude/radius, and θ is the angle (phase) in degrees, for example, 5L65 which is the same as 5*cis(65°).Įxample of multiplication of two imaginary numbers in the angle/polar/phasor notation: 10L45 * 3L90.įor use in education (for example, calculations of alternating currents at high school), you need a quick and precise complex number calculator.
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