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Let $z_{1}= 5-3i,\, z_{2}= x+yi.$ If $z_{1}-z_{2}= 2+7i$ then $x+y$ equals $\left (x,y\: \epsilon \, R \right )$

Option 1)
$-4$

Option 2)
$-5$

Option 3)
$-6$

Option 4)
$-7$

Answers (1)

$z_{1}-z_{2}=\left ( 5-3i \right )-\left ( x+iy \right )=\left ( 5-x \right )+\left ( -3-y \right )i$

But $z_{1}-z_{2}=2+7i$

$\therefore$ Using concept 713, we get

$5-x=2$ and $-3-y=7$

So, $x=3$ and $y=-10$

$\therefore x+y=-7$

$\therefore$ Option (D)

Subtraction of Complex Numbers -

(a+ib)-(c+id)=(a-c)+i(b-d)

-

Option 1)

$-4$

This is incorrect

Option 2)

$-5$

This is incorrect

Option 3)

$-6$

This is incorrect

Option 4)

$-7$

This is correct

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