Question

Let $z=x^2-7x-9ui$ such that $\overrightarrow{z}=y^{2}i-12$ then the number of orded pairs $(x,y)$ is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is D $4$

$z=x^2-7x-9ui$....$\left(1\right)$

$z=y^{2}i-12$....$\left(2\right)$

So, $\overline{z}=\overline{z}$

By equation $\left(1\right)$ and $\left(2\right)$

$\overline{(x^2-7n-9ui)}=y^{2}i=12$

$x^2-7n-9ui=y^{2}i=12$

By comparing Real and complex parts.

$y^2=9.4$

$y=\pm 3\sqrt{4}$

and

$x^2-7x=-12$

$x^2-7x+12=0$

$(x-3)(x-4)=0$

$x=3,4$

So, $x=3,4$ $y=\pm 3\sqrt{4}$

So, the number of orded parirs of $(x,y)$ is

$4$