Question

Complete the following equation. Your answers will be algebraic expressions. (a+bi)^2= _____ + 2abiHint: think of i as an ordinary variable and then replace i^2 with -1.

Answer 1

The given expression is:

`(a+ib)^2`

Expand to get:

`\begin{gathered} (a+ib)^2=a^2+i^2b^2+2abi \\ =a^2-b^2+2abi \end{gathered}`

The value is as above since it is given that i^2=-1.

So the expansion is:

`(a+ib)^2=a^2-b^2+2abi`

The blank should be:

`a^2-b^2`