WBJEE · Maths · Complex Number
The number of complex numbers \(\mathrm{p}\) such that \(|\mathrm{p}|=1\) and imaginary part of \(\mathrm{p}^{4}\) is 0, is
- A 4
- B 2
- C 8
- D infinitely many
Answer & Solution
Correct Answer
(A) 4
Step-by-step Solution
Detailed explanation
Hint: Let \(p=x+i y, p^{2}=\left(x^{2}-y^{2}\right)+2 i x y, p^{4}=\left(x^{2}-y^{2}\right)^{2}-4 x^{2} y^{2}+4 i x y\left(x^{2}-y^{2}\right)\) Now, \(x y\left(x^{2}-y^{2}\right)=0, \quad x=\pm y \Rightarrow y^{2}=\frac{1}{2} \Rightarrow y=\pm \frac{1}{\sqrt{2}}\) Four complex…
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