Question

Write this expression as a complex number in standard form, a + bi.
(-3√-81)(-5+ √-9) + 9i

Answer 1

81 + 144i

Explanation:

Original equation

`(-3√(-81))(-5+\sqrt-9) + 9i`

Rewrite the radicals

`(-3√(81) * √(-1))(-5+√(9) * √(-1)) + 9i`

Simplify the radicals

`(-3 * 9i)(-5+3i) + 9i`

Simplify further

`(-27i)(-5+3i) + 9i`

Distribute the -27i

`135i - 81i^2 + 9i`

Add like terms

`- 81i^2 + 144i`

Square the i

`- 81 * (-1) + 144i`

Simplify

`81 + 144i`