complex numbers

Question

division of complex numbers

Answer 1

Let’s divide two complex numbers z1/z2, where z1=a1+ib1 and z2=a2+ib2.

The conjugate of z2 is a2-ib2, so we multiply z1 and z2 by this conjugate:

(a1+ib1)(a2-ib2)/(a2²+b2²)=(a1a2+b1b2+i(a2b1-a1b2))/(a2²+b2²).

Call the quotient z3=(a1a2+b1b2)/(a2²+b2²)+i(a2b1-a1b2))/(a2²+b2²).