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Let z be a complex number satisfying equ...

Let `z` be a complex number satisfying equation `z^p-z^(-q)=0,\ where\ p ,q in N ,\t h e n` (A) if `p=q` , then number of solutions of equation will be infinite. (B) if `p=q` , then number of solutions of equation will be finite. (C) if `p!=q` , then number of solutions of equation will be `p+q+1.` (D) if `p!=q` , then number of solutions of equation will be `p+qdot`

A

if p=q, then number of solution of equation will infinte.

B

if p=q, then number of solutions of equaiton will finite

C

if `pne q`, then number of solutions of equaiton will `p+q+1`.

D

if `p ne q`, then number of solutions of equaiton will be `p+q`

Text Solution

Verified by Experts

The correct Answer is:
A, B
If q=p, then equation becomes `z^(p)= z^(-q)` and it has infinte
number of solutions because any z `in ` R will satisfly it. `p ne q`,
let `p gt q`, then `z^(p) = z^(-q)`
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