If-z-1-a-ib-and-z-2-c-id-are-complex-numbers-such-that-z-1-z-2-1-and-Re-z-1-z-2-0-then-the-pair-of-complex-numbers-1-a-ic-and-2-b-id-satisfy-1-1-1-2

Question Number 21005 by Tinkutara last updated on 10/Sep/17

If z_{1} = a + i b and z_{2} = c + i d are complex

numbers such that ∣ z_{1} ∣ = ∣ z_{2} ∣ = 1 and

Re (z_{1} {\bar{z}}_{2}) = 0, then the pair of complex

numbers ω_{1} = a + i c and ω_{2} = b + i d

satisfy

(1) ∣ ω_{1} ∣ = 1

(2) ∣ ω_{2} ∣ = 1

(3) Re (ω_{1} {\bar{ω}}_{2}) = 0

(4) ∣ ω_{1} ∣ = 2 ∣ ω_{2} ∣