Let w and z be two complex numbers such that w = a + ib and z = A + iB. The division of w by z is based on multiplying numerator and denominator by the complex conjugate of the denominator:

w / z = (a + ib) / (A + iB)

= (a + ib)(A - iB) / (A + iB)(A - iB)

= [ a A + b B + i(b A - a B) ] / [A^{ 2} + B^{ 2}]

= ( a A + b B )/ [A^{ 2} + B^{ 2}] + i (b A - a B) / [A^{ 2} + B^{ 2}]

How to use the calculator

Enter the real and imaginary parts (as an integer, a decimal or a fraction) of two complex numbers z and w and press "enter".