Question

Simplify the expression (3 – 3i)^3 by performing operations with pure imaginary numbers and complex numbers.1) -27 + 216i2) -27 + 54i3) -54 – 216i4) -54 – 54i

Answer 1

`-54-54i`

Step-by-step explanation

We want to simplify the expression given:

`(3-3i)^3`

To do this, we have:

`(3-3i)(3-3i)(3-3i)`

Multiply two of the expressions in brackets and then simplify by multiplying the result with the last expression:

`\begin{gathered} (3-3i)(9-9i-9i-9) \\ \Rightarrow(3-3i)(-18i) \\ \Rightarrow-54i-54 \\ \Rightarrow-54-54i \end{gathered}`

That is the answer.