If z1 is a complex number other than –1 such that |z1| = 1 and z2 = then show that z2 is purely imaginary.

Let z1 = a + ib such that | z1| = √(a2 + b2) = 1Now, Thus, the real part of z2 is 0 and z2 is purely imaginary.

Q9 of 202 Page 188

If z₁ is a complex number other than –1 such that |z₁| = 1 and z₂ = then show that z2 is purely imaginary.

Let z₁ = a + ib such that | z₁| = √(a² + b²) = 1

Now,

Thus, the real part of z₂ is 0 and z₂ is purely imaginary.

If z² + |z|² = 0, show that z is purely imaginary.

If is purely imaginary and z = –1, show that |z| = 1.

For all z C, prove that

(i)

(ii) .

(iii) = |z|²

(iv) is real

(v) is 0 or imaginary.

If z₁ = (1 + i) and z₂ = (–2 + 4i), prove that Im