Get Answers to all your Questions

header-bg qa

Number of solution of the equation z^{3}+\frac{3(\overline{z})^{2}}{\left | z \right |}=0  where z is a complex number is

Option: 1

2


Option: 2

3


Option: 3

6


Option: 4

5


Answers (1)

best_answer

 

Euler's Form of a Complex number -

z=re^{i\theta}

- wherein

r denotes modulus of z and \theta denotes argument of z.

 

 

z^{3}+\frac{3(\overline{z})^{2}}{\left | z \right |}=0             Let z=re^{i\theta }

\Rightarrow r^{3}e^{i3\theta}+3re^{-2\theta }=0

Since ‘r’ cannot be zero

\Rightarrow r^{2}e^{i5\theta}=-3                 modulus=3  which will hold for 

    r=\sqrt{3}  and 5 distinct values of ‘\theta

Thus there are five solution.

Posted by

Ritika Jonwal

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE