Question

Evaluate the expression ( 1 + 2 i ) ( − 2 − 1 i ) and write the result in the form a + b i .

Answer 1

- 5i.

Explanation:

( 1 + 2 i ) ( − 2 − 1 i )

= 1 * -2 + 1*-1i + 2i*-2 - 2i*1i

= -2 - i - 4i - 2i^2 i^2 = -1 so we have:

-2 - 5i +2

= 0 - 5i

= -5i.