If x-iy2-3i-4-i 12 then x - y -

The correct option is A 32 (x+iy)(2 3i)=4+i12 2x+2iy 3ix+3y=4+i2 2x+3y+i(2y 3x)=4+i2 Hence 2x+3y=4 ................................(i) ...

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Standard X

Mathematics

Equation Reducible to Linear Equations in Two Variables

If x+iy2-3i...

Question

If $(x + i y) (2 - 3 i) = 4 + i (\frac{1}{2})$ then $x + y =$

\frac{3}{2}

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\frac{1}{2}

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0

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\frac{2}{3}

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Solution

The correct option is A $\frac{3}{2}$
$(x + i y) (2 - 3 i) = 4 + i \frac{1}{2}$
$2 x + 2 i y - 3 i x + 3 y = 4 + \frac{i}{2}$
$2 x + 3 y + i (2 y - 3 x) = 4 + \frac{i}{2}$
Hence
$2 x + 3 y = 4$ ................................(i)
And
$2 y - 3 x = \frac{1}{2}$ .............................(ii)
Solving both the equations give us
$y = 1$
$x = \frac{1}{2}$
Hence
$x + y$
$= 1 + \frac{1}{2}$
$= \frac{3}{2}$ .

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If (x+iy)(2−3i)=4+i(12) then x+y=

The correct option is A 32(x+iy)(2−3i)=4+i122x+2iy−3ix+3y=4+i22x+3y+i(2y−3x)=4+i2Hence 2x+3y=4 ................................(i)And 2y−3x=12 .............................(ii)Solving both the equations give us y=1x=12Hence x+y=1+12=32.

If $(x + i y) (2 - 3 i) = 4 + i (\frac{1}{2})$ then $x + y =$