Question

answer that 5th question​

Answer 1

We know that

zz = |z|²

Given:

z = iz² ...(1)

Taking mod on both sides, we

get

|z| = |z|²

⇒ |z| = 0 or |z| =1

It is given the z is a non-zero number, therefore |z| = 1

Now,

Multiply (1) both sides with with z, we get

zz = iz³

⇒ |z|² = iz³

⇒ z³ -i

⇒ z³ - 1³ = 0

⇒ (z − i) (z² + iz − 1) = 0

Hence

z = i and z² + iz - 1 = 0

z²+iz-1=0 Gives

-it√-1+4 2

-i± √3 2 N

So z can be (0, 1) or ± √3 2 1 - 2