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. The division of two complex numbers can be accomplished by multiplying the numerator and denominator by the denominator's complex conjugate. 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 absolute value or modulus is the distance of the image of a complex number from the origin in the plane. The calculator uses the Pythagorean theorem to find this distance. Square root of complex number (a+bi) is z, if z 2 = (a+bi). Because of the fundamental theorem of algebra, you will always have two different square roots for a given number. If you want to find out the possible values, the easiest way is to go with De Moivre's formula. We calculate all complex roots from any number - even in expressions: Our calculator is on edge because the square root is not a well-defined function on a complex number. Our calculator can power any complex number to an integer (positive, negative), real, or even complex number. In other words, we calculate 'complex number to a complex power' or 'complex number raised to a power'.

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