JEE Mains · Maths · STD 11 - 4.1 complex nubers
If \(z =2+3 i\), then \(z ^{5}+(\overline{ z })^{5}\) is equal to.
- A \(244\)
- B \(224\)
- C \(245\)
- D \(265\)
Answer & Solution
Correct Answer
(A) \(244\)
Step-by-step Solution
Detailed explanation
\(z^{5}+(\bar{z})^{5}=(2+3 i)^{5}+(2-3 i)^{5}\) \(=2\left({ }^{5} C_{0} 2^{5}+{ }^{5} C_{2} 2^{3}(3 i)^{2}+{ }^{5} C_{4} 2^{1}(3 i)^{4}\right)\) \(=2(32+10 \times 8(-9)+5 \times 2 \times 81)=244\)
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