Q15 of 66 Page 91

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

Let z = x + iy


Now,




Given that is purely imaginary.



⇒ x2 – 1 + y2 = 0


⇒ x2 + y2 = 1



∴ |z| = 1


More from this chapter

All 66 →
13

If arg (z – 1) = arg (z + 3i), then find x – 1 : y. where z = x + iy

 14

Show that represents a circle. Find its centre and radius.

 16

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

17

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