If-z-satisfies-z-1-lt-z-3-then-2z-3-i-satisfies-1-5-i-lt-3-i-2-5-lt-3-3-Im-i-gt-1-4-arg-1-lt-pi-2-

Question Number 20934 by Tinkutara last updated on 08/Sep/17

If z satisfies ∣ z - 1 ∣ < ∣ z + 3 ∣, then ω =

2 z + 3 - i satisfies

(1) ∣ ω - 5 - i ∣ < ∣ ω + 3 + i ∣

(2) ∣ ω - 5 ∣ < ∣ ω + 3 ∣

(3) Im (i ω) > 1

(4) ∣ \arg (ω - 1) ∣ < \frac{π}{2}

Commented by Tinkutara last updated on 10/Sep/17

help pls