Question

The number of complex numbers \(p\) such that \(|p|=1\) and imaginary part of \(p^{4}\) is 0 , is
(A) 4
(B) 2
(C) 8
(D) infinitely many

Answer 1

Ans : (A)
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 numbers.

Answer 2

coupon for cialis <a href="https://ordergnonline.com/">tadalafil 5 mg tablet</a> buy ed medications