MHT CET · Maths · Complex Number
Let z be the complex number with \(\operatorname{Im}(\mathrm{z})=10\) and satisfing \(\frac{2 \mathrm{z}-\mathrm{n}}{2 \mathrm{z}+\mathrm{n}}=2 i-1\), where \(i=\sqrt{-1}\), for some natural number ' n ' then
- A \(\mathrm{n}=20\) and \(\operatorname{Re}(\mathrm{z})=10\)
- B \(\mathrm{n}=20\) and \(\operatorname{Re}(\mathrm{z})=-10\)
- C \(\mathrm{n}=40\) and \(\operatorname{Re}(\mathrm{z})=10\)
- D \(\mathrm{n}=40\) and \(\operatorname{Re}(\mathrm{z})=-10\)
Answer & Solution
Correct Answer
(D) \(\mathrm{n}=40\) and \(\operatorname{Re}(\mathrm{z})=-10\)
Step-by-step Solution
Detailed explanation
\(2z - n = (2i - 1)(2z + n)\) \(2z - (2i - 1)2z = n + (2i - 1)n\)
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