Thursday, June 14, 2012

Complex Numbers - Division

If z1 = a+ib and z2 = c+id are two complex numbers , then their division z1 / z2 can be expressed as [(ac + bd)+i(bc - ad)] / (c2 + d2). This achieved by multiplying and dividing the numerator and denominator by conjugate of the denominator.

Let us see what happens geometrically when we divide two complex numbers? Let us express complex numbers in their polar form. With this approach we find the division of two complex numbers   w = r (cos α + i sin α) and z = s (cos β + i sin β) is given by w / z = r * [(cos (α- β) + i sin (α - β)] / s.

This means that, when dividing two complex numbers w and z, we divide their moduli and we subtract the angles which w and z make with the positive x-direction.

This is a Java Applet created using GeoGebra from - it looks like you don't have Java installed, please go to

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