Let $z$ be those complex numbers which satisfy $|z+5| \leq 4$ and $z(1+i)+\bar{z}(1-i) \geq-10, i=\sqrt{-1}.$ If the maximum value of $|z+1|^2$ is $\alpha+\beta \sqrt{2}$, then the value of $(\alpha+\beta)$ is ____. Where $\alpha \& \beta$ are natural numbers.

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Hard

1 of 1

Analyzing +4 | -1

Let

z

be those complex numbers which satisfy

|z+5| \leq 4

and

z(1+i)+\bar{z}(1-i) \geq-10, i=\sqrt{-1}.

If the maximum value of

|z+1|^2

\alpha+\beta \sqrt{2}

, then the value of

(\alpha+\beta)

is ____. Where

\alpha \& \beta

are natural numbers.

View answer and explanation

Correct option: B

Option B (48) is correct because by substituting

z = x + iy

into the given conditions, we find the region in the complex plane and maximize

|z+1|^2