Question

Complete the following equations. Your answers will be algebraic expressions. (a+bi)(a-bi)= ______ + ______i(a+bi)^2-(a-bi)^2= _____ + _____i

Answer 1

Given:

1) the expression is,

$\begin{gathered} (a+ib)(a-ib) \\ =a(a-ib)+ib(a-ib) \\ =a^2-iab+iab-(i^2)b \\ =a^2-(-1)b^2\ldots\ldots\ldots\ldots.(\sin cei^2=-1) \\ =a^2+b^2 \end{gathered}$

2)

$(a+ib)^2-(a-ib)^2$