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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

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ANSWER

[tex]-54-54i[/tex]

EXPLANATION

We want to simplify the expression given:

[tex](3-3i)^3[/tex]

To do this, we have:

[tex](3-3i)(3-3i)(3-3i)[/tex]

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

[tex]\begin{gathered} (3-3i)(9-9i-9i-9) \\ \Rightarrow(3-3i)(-18i) \\ \Rightarrow-54i-54 \\ \Rightarrow-54-54i \end{gathered}[/tex]

That is the answer.

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