If $z$ is a complex number such that $z \ne 0$ and ${\rm{Re\;}}\left( {\rm{z}} \right) = 0,$ then

${\rm{Re\;}}\left( {{{\rm{z}}^2}} \right) = 0$

${\rm{Re\;}}\left( {{z^2}} \right) = {\rm{Im\;}}\left( {{z^2}} \right)$

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Easy

1 of 1

Application +4 | -1

z

is a complex number such that

z \ne 0

and

\mathrm{Re\;}\left( \mathrm{z} \right) = 0,

then

View answer and explanation

Correct option: B

\mathrm{Im\;}\left( {{z^2}} \right) = 0

Option B (

\mathrm{Im\\;}\left( {{{{z}}^2}} \right) = 0

) is correct because if the real part of z is 0, then z is purely imaginary, and the square of a purely imaginary number is a real number, thus having an imaginary part of 0.

More Questions from COMPLEX NUMBERS

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The number of non-zero integer solutions of the equation

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is If

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, then for any complex number

z, \frac{z}{1-z^2}

Let

\left|z_r-r\right| \leq r, \forall r=1,2,3, \ldots, n

, then

\left|\sum\limits_{r=1}^n z_r\right|

is less than The roots of the cubic equation

(z+a b)^3=a^3

, where

a \neq 0

represents the vertices of a triangle. If

\alpha, \beta

and

\gamma

are the roots, then find the value of

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. Number of solutions of the equation

{z^2} + {\left| z \right|^2} = 0,

where

z \in C

is If

2x = - 1 + \sqrt 3 i

, then the value of

{\left( {1 - {x^2} + x} \right)^6} - {\left( {1 - x + {x^2}} \right)^6}

is equal to