Question

The real values of $x$ and $y$ for which the following equality hold, are respectively $(x^{4}+2xi)-(3x^{2}+iy)=(3-5i)+(1+2iy)$

• A. $2, 3$ or $-2$, $1/3$
• B. $1$, $3$ or $-1$, $1/3$
• C. $2$, $1/3$ or $-2$, $3$
• D. $2$, $1/3$ or $-2$, $-1/3$

Answer 1

Answer: (A)

$2, 3$ or $-2$, $1/3$

Answer 2

The given equality can be rewritten as $\left(x^{4}-3x^{2}\right)+i\left(2x-y\right)$ $=4+i\left(2y-5\right)$ $\Rightarrow\, x^{4}-3x^{2}=4$ , $2x-y=2y-5$ $\Rightarrow\,\left(x^{2}-4\right)\left(x^{2}+1\right)=0$ $\Rightarrow x=\pm\,2$ $\left(\because\quad x^{2}\ne-1\right)$ $\therefore\,$ At $x=2$ , $y=3$ and at $x=-2$ , $y=1 /3$