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Grade: 11

                        

if |z1| = |z2| and arg(z1/z2) = pi then z1+z2 is equal to a) 0 b) Purely Imaginary c) Purely Real d) None [Ans. a) 0]

8 months ago

Answers : (1)

Arun
24742 Points
							
Let |z1| = |z2| = r ,
and arg(z2) = A
Given, arg(z1) - arg(z2) = π
arg(z1) = π + arg(z2)
arg(z1) = π + A
So, z2 = r cos(A) + i sin(A)
z1 = r cos(π + A) + i sin(π + A)
z1 = - [r cos(A) + i sin (A)]
z1 = - z2
z1 + z2 = 0.
8 months ago
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