Question

The real order pair $(x,y)$ which satisfies $(x^4+2xi)-(3x^2+yi)=(3-5i)+(1+2yi)$ is

• A. $(-2,\frac{1}{3})$
• B. $(2,3)$
• C. $(-2,3)$
• D. $(2,\frac{1}{3})$

Answer 1

Answer: (A), (B)

$(2,3)$

Given $(x^4+2xi)-(3x^2+yi)=(3-5i)+(1+2yi)$
$\Rightarrow (x^4-3x^2)+i(2x-3y)=4-5i$
Equating real and imaginary parts, we get
$x^4-3x^2=4\Rightarrow (x^2-4)(x^2+1)=0\Rightarrow x^2=4(\because x^2+1\ne 0)\Rightarrow x=\pm 2$
And
$2x-3y=-5\Rightarrow y=3,\frac{1}{3}$
Hence $(x,y)\equiv (2,3),(-2,\frac{1}{3})$