If z 0 is a complex number, then - Vidyadip

MCQ

If $z \ne 0$ is a complex number, then

✓
${\mathop{\rm Re}\nolimits} (z) = 0 \Rightarrow {\mathop{\rm Im}\nolimits} ({z^2}) = 0$
B
${\mathop{\rm Re}\nolimits} ({z^2}) = 0 \Rightarrow {\mathop{\rm Im}\nolimits} ({z^2}) = 0$
C
${\mathop{\rm Re}\nolimits} (z) = 0 \Rightarrow {\mathop{\rm Re}\nolimits} ({z^2}) = 0$
D
None of these

✓

Answer

Correct option: A.

${\mathop{\rm Re}\nolimits} (z) = 0 \Rightarrow {\mathop{\rm Im}\nolimits} ({z^2}) = 0$

a
(a) If $z \ne 0$. Let $z = x + iy$ ==> ${z^2} = {x^2} - {y^2} + i(2xy)$
$Re(z)= 0$ ==> $x = 0$. Therefore ${\mathop{\rm Im}\nolimits} ({z^2}) = 2xy = 0$
Thus ${\mathop{\rm Re}\nolimits} (z) = 0 \Rightarrow {\mathop{\rm Im}\nolimits} ({z^2}) = 0$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from 4.1 complex nubers→4.1 complex nubers — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The probability of happening an event $A$ is $0.5$ and that of $B$ is $0.3$. If $A$ and $B$ are mutually exclusive events, then the probability of happening neither $A$ nor $B$ is

Let $A(a, b), B(3,4)$ and $(-6,-8)$ respectively denote the centroid, circumcentre and orthocentre of a triangle. Then, the distance of the point $P(2 a+3,7 b+5)$ from the line $2 x+3 y-4=0$ measured parallel to the line $x-2 y-1=0$ is

The sum of the squares deviations for 10 observations taken from their mean 50 is 250. The coefficient of variation is:

If $a _{1}, a _{2}, a _{3} \ldots$ and $b _{1}, b _{2}, b _{3} \ldots$ are $A.P.$ and $a_{1}=2, a_{10}=3, a_{1} b_{1}=1=a_{10} b_{10}$ then $a_{4} b_{4}$ is equal to

In $\Delta ABC$, if $a, b, c$ are in $A.P.$ (with usual notations), identify the incorrect statements -

Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?

The length of the latus-rectum of the parabola $4 y^2+2 x-20 y+17=0$ is

The value of $\sin^25^\circ+\sin^210^\circ+\sin^215^\circ+\ ...\ +\sin^285^\circ+\sin^290^\circ$ is:

The mean of the following data is :
45, 35, 20, 30, 15, 25, 40:

The values of k for which the quadratic equation $k x^2+1=k x+3 x-11 x^2$ has real and equal roots are: