Simplifying Complex Expressions| Algebra| ENGG10 LE2 Problem 4

Perform the indicated operations, and write your final answer in the form a+bi.

\left(2+\sqrt{-9}\right)^4

SOLUTION:

\left(2+\sqrt{-9}\right)^4

=\left(2+3i\right)^4

=1\left(2\right)^4\left(3i\right)^0+4\left(2\right)^3\left(3i\right)^1+6\left(2\right)^2\left(3i\right)^2+4\left(2\right)^1\left(3i\right)^3+1\left(2\right)^0\left(3i\right)^4

=16+96i+216i^2+216i^3+81i^4

=16+96i-216-216i+81

=-119-120i