JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let \(z_1\) and \(z_2\) be two complex number such that \(z_1\) \(+z_2=5\) and \(z_1^3+z_2^3=20+15 i\). Then \(\left|z_1^4+z_2^4\right|\) equals-
- A \(30 \sqrt{3}\)
- B \(75\)
- C \(15 \sqrt{15}\)
- D \(25 \sqrt{3}\)
Answer & Solution
Correct Answer
(B) \(75\)
Step-by-step Solution
Detailed explanation
\(z_1+z_2=5\) \(z_1^3+z_2^3=20+15 i\) \(z_1^3+z_2^3=\left(z_1+z_2\right)^3-3 z_1 z_2\left(z_1+z_2\right)\) \(z_1^3+z_2^3=125-3 z_1 \cdot z_2(5)\) \(\Rightarrow 20+15 i=125-15 z_1 z_2\) \(\Rightarrow 3 z_1 z_2=25-4-3 i\) \(\Rightarrow 3 z_1 z_2=21-3 i\)…
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