If |z1| = 1 (z1 ≠ –1) and then show that the real part of z2 is zero.

Let z1 = x + iyNow, Since x2 + y2 = 1∴ Hence, the real part of z2 is zero.

Q17 of 66 Page 91

If |z₁| = 1 (z₁ ≠ –1) and then show that the real part of z₂ is zero.

Let z₁ = x + iy

Now,

Since x² + y² = 1

∴ Hence, the real part of z₂ is zero.

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

z₁ and z₂ are two complex numbers such that |z₁| = |z₂| and arg (z₁) + arg (z₂) = π, then show that

If z₁, z₂ and z₃, z₄ are two pairs of conjugate complex numbers, then find

If |z₁| = |z₂| = ….. = |z_n| = 1, then

Show that |z₁ + z₂ + z₃ + …. + z_n|