Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# Find the Real Value of X and Y, If ( 1 + I ) ( X + I Y ) = 2 − 5 I - Mathematics

Find the real value of x and y, if

$(1 + i)(x + iy) = 2 - 5i$

#### Solution

$\left( 1 + i \right)\left( x + iy \right) = 2 - 5i$

$\Rightarrow x + iy + ix + i^2 y = 2 - 5i$

$\Rightarrow x + iy + ix - y = 2 - 5i$

$\Rightarrow \left( x - y \right) + i\left( y + x \right) = 2 - 5i$

$\text { Comparing both the sides },$

$x - y = 2 . . . (1)$

$x + y = - 5 . . . (2)$

$\text { Adding equations (1) and (2) },$

$2x = - 3$

$\Rightarrow x = \frac{- 3}{2}$

$\text { Substituting the value of x in equation (1) },$

$\frac{- 3}{2} - y = 2$

$\Rightarrow y = \frac{- 3}{2} - 2$

$\Rightarrow y = \frac{- 7}{2}$

$\therefore x = \frac{- 3}{2} \text { and y } = \frac{- 7}{2}$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 13 Complex Numbers
Exercise 13.2 | Q 2.4 | Page 31

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