Q

Help me understand! - Complex numbers and quadratic equations - JEE Main-8

If $2x+i\left ( 3y-1 \right )= -8-16i$  then  $x+y$  equals  $\left ( Where\: x,y\, \epsilon \, R \right )$

• Option 1)

$-6$

• Option 2)

$-7$

• Option 3)

$-8$

• Option 4)

$-9$

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Two complex numbers are equal when their corresponding real parts and corresponding imaginary parts both are simultaneously equal.

$\therefore \: 2x=-8\: \Rightarrow \: x=-4$

and,  $3y-1=-16\: \Rightarrow \, y=-5$

$\therefore x+y=-9$

Equality in Complex Numbers -

z=x+iy & w=a+ib are equal iff x=a & y=b

- wherein

Two complex numbers are equal iff real parts as well as imaginary parts are equal.

Option 1)

$-6$

This is incorrect

Option 2)

$-7$

This is incorrect

Option 3)

$-8$

This is incorrect

Option 4)

$-9$

This is correct

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