If z and are two non-zero complex numbers such that |z |=1 , and (z)- ( )= 2 , then find the value of 5 i z .

Step-by-step solution

Let z=r₁ e^ i and w=r₂ e^ i z = r ₁ e ^ -1 Given, |z |=1 |r₁ e^ i r₂ e^ i |=1 r₁ r₂=1 .....(i) and (z)- ( )= 2 - = 2 Then, z =r₁ e^ -i r₂ e^ i =r₁ r₂ e^ -i( - ) From Eqs. (i) and (ii), we get z =1 e^ -i / 2 = 2 - i 2 z =-i