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

Question

Dr. Abubacker · Accepted Answer

(d)
Given,
$z = \frac{11 - 3i}{1 + i} 	imes \frac{1 - i}{1 - i} = \frac{8 - 14i}{2} = 4 - 7i$
Since, $z = i\alpha$ is real, therefore $4 - 7i - i\alpha$ is real, if $\alpha = - 7$

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

Explanation

Reviewed by Dr. Abubacker

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