Question

Write this expression as a complex number in standard form

Answer 1

Answer: 81+144i

Explanation:

Answer 2

`81+144i`

Explanation:

We want to simplify:

`\displaystyle (-3√(-81))(-5+√(-9)) + 9i`

Recall that:

`\displaystyle √(-a) = i√(a)`

Therefore:

`\displaystyle \begin{aligned} (-3√(-81))(-5+√(-9)) + 9i & = (-3i√(81))(-5+i√(9))+9i \\ \\ &= -(3i(9))(-5+i(3))+9i \\ \\ & = -27i(-5+3i)+9i \\ \\ & = 135i -81i^2 + 9i \\ \\ & = 144i - 81i^2 \\ \\ & = 81+144i\end{aligned}`

Note that i² = -1.

In conclusion:

`\displaystyle (-3√(-81))(-5+√(-9))+9i = 81 + 144i`