TS EAMCET · Maths · Complex Number
If \(z=1-\sqrt{3} i\), then \(z^3-3 z^2+3 z=\)
- A 0
- B \(1+3 \sqrt{3} i\)
- C 1
- D \(2+3 \sqrt{3} i\)
Answer & Solution
Correct Answer
(B) \(1+3 \sqrt{3} i\)
Step-by-step Solution
Detailed explanation
Given, \(z=1-\sqrt{3} i\) \(\begin{aligned} & z^2=1+3 i^2-2 \sqrt{3} i=-2(1+\sqrt{3} i) \\ & z^3=-2(1+\sqrt{3} i)(1-\sqrt{3} i)=-8 \end{aligned}\) Now, \(z^3-3 z^2+3 z=-8+6+6 \sqrt{3} i+3-3 \sqrt{3} i=1+3 \sqrt{3} i\).
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