If z and ω are two complex numbers such that z ω = 1 and a r g z - a r g ( ω ) = π 2 , then:

Step-by-step solution

Let z = r and a r g z = θ , given a r g z - a r g ω = π 2 ⇒ θ - a r g ω = π 2 ⇒ a r g ω = θ - π 2 We know that, if z = r   &   a r g z = θ then 1 z = 1 r   &   a r g z ¯ = - a r g z = - θ , Hence, ω = 1 r and a r g ( ω ¯ ) = - a r g ω = π 2 - θ Now, by using Euler form i.e. if z = r   &   a r g z = θ , then z = r e i θ , we have z = r e i θ and ω = 1 r e