Let z 1 and z 2 be two complex numbers such that z ¯ 1 = i z ¯ 2 and arg z 1 z ¯ 2 = π , then the argument of z 1 is

Step-by-step solution

z ¯ 1 = i z ¯ 2     ⇒ z 1 = - i z 2     ⇒ i z 1 = z 2 ⇒ e i π 2 z 1 = z 2 Given, arg z 1 z ¯ 2 = π Let z 1 = r e i θ       ⇒     z 2 ¯ = r e - i π 2 + θ So arg e i 2 θ + π 2 = π       ⇒     2 θ + π 2 = π ⇒       θ = π 4