Question

Write the correct letter from column (2) against column (1):
$C_1$ $C_2$
(a)$Rez=0$ (i)$Re{z}^2=0$
(b)$Argz=\pi /4$ (ii)$Im{z}^2=0$
(iii)$Re{z}^2=Im{z}^2$.

• A. a=(i), b=(ii)
• B. a=(ii), b=(iii)
• C. a=(ii), b=(i)
• D. a=(iii), b=(ii)

Answer 1

The correct option is C a=(ii), b=(i)

Ans. (a)$\to$(ii) (b)$\to$(i)
(a)$\Rightarrow Rez=0\Rightarrow x=0$
(b)$\Rightarrow Argz=\pi /4\Rightarrow \tan {}^{-1}\left(y/x\right)=\pi /4$

$\therefore y=x$
Now$z^2=y^2+i\left(2xy\right)=-y^2+i\cdot 0,$
i.e when $x=0$ $\therefore Im{z}^2=0$ $\to$ (ii)
Again $z^2=0+i\left(2x^2\right)$, by (2) as $y=x$
$\therefore Re{z}^2=0$ i.e (i)