Question

A complex number Z satisfies the equation $|z^2-9|+|z^2|=41$ then the which of the following is/are true

• A. |z+3|+|z-3|=8
• B. |z+3|+|z-3|=10
• C. Maximum value of |z| is 5
• D. Maximum value of |z| is 6

Answer 1

Answer: (B), (C)

The correct options are
B |z+3|+|z-3|=10
C Maximum value of |z| is 5

$(|z+3|+|z-3|{)}^2=|z+3{|}^2+|z-3{|}^2+2|z^2-9|=2|z{|}^2+18+2|z^2-9|$
=100
$\Rightarrow |z+3|+|z-3|=10\Rightarrow ellipse2a=10\Rightarrow a=5$
$\therefore$ Max value of |z| is 5