JEE Main 2026 Apr 2 Shift 1, Mathematics Q2: Introduction to Complex Numbers And Their Conjugates

JEE Main2026Apr 2, Shift 1Mathematics

Let $x$ and $y$ be real numbers such that $50 (\frac{2 x}{1 + 3 i} - \frac{y}{1 - 2 i}) = 31 + 17 i$ , $i = - 1$ . Then the value of $10 (x - 3 y)$ is :

A
$20$
B
$31$
C
$35$
D
$75$

Solution

Rationalise each fraction. $\frac{2 x}{1 + 3 i} = \frac{2 x ( 1 - 3 i )}{10}$ and $\frac{y}{1 - 2 i} = \frac{y ( 1 + 2 i )}{5}$ . Substituting and multiplying through by $50$ :

$50 \cdot \frac{2 x ( 1 - 3 i )}{10} - 50 \cdot \frac{y ( 1 + 2 i )}{5} = 31 + 17 i$

$10 x (1 - 3 i) - 10 y (1 + 2 i) = 31 + 17 i$

Separate real and imaginary parts:

Real: $10 x - 10 y = 31$ ; Imaginary: $- 30 x - 20 y = 17$ .

Multiply the real equation by $3$ and add to the imaginary: $- 50 y = 110 \Rightarrow y = - 2.2$ , hence $x = 0.9$ .

$∴ 10 (x - 3 y) = 10 (0.9 + 6.6) = 75$

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JEE Main 2026 Apr 2 Shift 1, Mathematics Q2: Introduction to Complex Numbers And Their Conjugates

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