Question

How do you evaluate `1+ ( 1+ i ) + ( 1+ i ) ^ { 2} + ( 1+ i ) ^ { 3}`?

Answer 1

`5i`

Explanation:

`1+(1+i)+(1+i)^2+(1+i)^3`

=`[(1+i)^4-1]/[(1+i)-1]`

=`(i^4+4i^3+6i^2+4i)/i`

=`i^3+4i^2+6i+4`

=`-i-4+6i+4`

=`5i`