Wednesday, June 13, 2012

Complex Numbers - Multiplication

If z1 = a+ib and z2 = r+is are two complex numbers , then their multiplication           z1 * z2 can be expressed as [(ar - bs)+i(as+br)].

 Let us see what happens geometrically when we multiply two complex numbers? To answer this question, it is advantageous to express complex numbers in their polar form.

With this approach we find that the product 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 s [(cos (α+β) + i sin (α+β)].

This means that, when multiplying two complex numbers w and z, we multiply their moduli and we add 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


  1. ooo... that helped a lot. thank you sir

  2. A number which can be put in the form a + bi termed as complex number, where a and b are real numbers and i is called the imaginary unit,in given expression "a" is the real part and b is the imaginary part of the complex number. The complex number can be identified with the point (a, b).