Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If 
is a complex number such that 
, then find the value of 
, so that equation 
has one purely imaginary root.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Sol. We have, 
........(i)
On taking conjugate both sides, we get
[since, 
is purely imaginary, 
]
or 
........(ii)
Eliminating 
from Eqs. (i) and (ii) by cross-multiplication rule, we get
On dividing each by 4, we get
or 
.......(iii)
Given, 
Let 
Then, from Eq. (iii), we get
Only feasible value of 
Hence, 
, where 
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