AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Offline Centres

Let $S_{1} :$ The complex number ${(e^{3})}^{i}$ lies in the third quadrant.
$S_{2} :$ If $| z_{1} | - | z_{2} | = | z_{1} + z_{2} |$ for some complex numbers $z_{1}$ and $z_{2}$ , then $z_{2}$ must be 0.
$S_{3} :$ For distinct complex numbers $z_{1}$ and $z_{2}$ . the equation $| {(z - z_{1})}^{2} | = | {(z - z_{2})}^{2} |$ has at most 4 solutions.
$S_{4} :$ $Im z_{1} \neq 0$ and $Im z_{2} \neq 0$ Then ${(Z_{1})}^{Z_{2}}$ is always a non real complex number.
The number of TRUE statements among the $S_{1}, S_{2}, S_{3}, S_{4}$

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

answer is A.

(Unlock A.I Detailed Solution for FREE)

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$S_{1} : 3 \in Q_{2} S_{2} : Z_{1} = i = Z_{2}$

Watch 3-min video & get full concept clarity

No courses found

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test