Question

Rationalize the denominator of 10 over 8 - 5i?

Answer 1

For rationalizing the denominator when the denominator is complex, you simply multiply both top and bottom by the "complex conjugate" of the denominator. The complex conjugate means you take the a+bi and change the + to a -. so in this case the complex conjugate is 8+5i. Multiply both top and bottom by this and you get
10(8+5i)/((8-5i)(8+5i))=(80+40i)/(64+25)=(80+40i)/89, or 80/89 + 40/89 i