Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Let 
and c be any three non-zero complex numbers. If 
and ' z ' satisfies the equation 
; prove that 
and 
.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Sol. If |z| = 1 ⇒ z. 
= 1 or 
= 
We have, az 2 + bz + c = 0 … (i)
Taking conjugates on both sides, we get
+ 
+ 
= 0 … (ii)
Replacing 
= 
in (ii), we get
(z) 2 + 
z + 
= 0 … (iii)
Now, (i) and (iii) must be identical equations;
⇒ 
= 
= 
a. 
and 
b = c 
… (iv)
from 
.b = c. 
, we get;
a 
b 
= a( 
) 2 c
|a| |b| = 
and |a| = |c| {using (iv)}
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