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

\[(1 + i)(x + iy) = 2 - 5i\]

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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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