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  4. Let z=(11-3i/1+i). If a is a real number such that z-iα is real, then the value of α is

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Q. Let $ z=\frac{11-3i}{1+i}. $ If a is a real number such that $ z-i\alpha $ is real, then the value of $ \alpha $ is

KEAMKEAM 2007Complex Numbers and Quadratic Equations

Solution:

$ \because $ $ z=\frac{11-3i}{1+i}\times \frac{1-i}{1-i} $
$=\frac{11-11i-3i-3}{1+1} $
$=\frac{8-14i}{2}=4-7i $
Also, $ \alpha $ is a real number such that $ z-i\alpha $ is real.
$ \therefore $ $ 4-7i-i\alpha $ is real, if $ \alpha =-7 $ .