Write the complex number in the polar form.
Let z = i -1 = -1 + i = r() ....(i)
r cos
= - 1 ...(ii)
r sin = 1 ...(iii)
Squaring and adding (ii) and (iii) we get
r2 = 2 r =
∴ From (ii) and (iii).
∴
Which is the reequired polar form.
A complex number z is said to be unimodular, if |z|= 1. suppose z1 and z2 are complex numbers such that is unimodular and z2 is not unimodular. Then, the point z1 lies on a
straight line parallel to X -axis
straight line parallel to Y -axis
circle of radius 2
circle of radius 2