If is purely imaginary number (z ≠ – 1), find the value of |z|.

Question

Philoid · Accepted Answer

Given:

⇒ is purely imaginary

⇒ Let us assume , where K is any real number

Let us assume z=x+iy

⇒

Multiplying and dividing with (x+1)-iy

⇒

We know that i²=-1

⇒

Equating Real and Imaginary parts on both sides we get

⇒

⇒ x²+y²-1=0

⇒ x²+y²=1

⇒

⇒ |z|=1

∴ |z|=1