Find the product of

Question

(10 − 4i) and its conjugate.

Answer 1

For any complex number z=x+iy in rectangular form, its complex conjugate is

¯z =x−iy.

It can be shown that the product of a complex number with its complex conjugate is a real number given by

z¯z=x2+y2.

So:

(10-4i) x (10+4i) = 10² + 4²

116 + 0i

116

Answer 2

Conjugates are defined as a pair of binomials with identical terms but opposite operations. The conjugate of (10 - 4i) is (10 + 4i). To find the product, multiply the terms and distribute.

(10 - 4i) (10 + 4i)

= (10)² + (10)(-4i) + (10)(+4i) + (-4i)(+4i)

= 100 - 40i + 40i - 16i²

= 100 - 16(-1)

= 100 +16

= 116

Answer = 116