If z1 is a complex number other than -1 such that |z1| = 1 and then show that the real parts of z2 is zero.

Question

If z1 is a complex number other than -1 such that |z1| = 1 and  then show that the real parts of z2 is zero.

Philoid · Accepted Answer

Given:⇒ Let us assume z1=x+iy⇒ |Z1|=1⇒ ⇒ x2+y2=1-------------------(1)⇒ ⇒ ⇒ ⇒ ⇒ We know that i2=-1⇒ ⇒ ⇒ ⇒ ⇒ ∴ z2 is an imaginary one.

If z₁ is a complex number other than -1 such that |z₁| = 1 and then show that the real parts of z₂ is zero.