The real values of x and y for which the equa | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given equation: $(x + iy)(2 - 3i) = 4 + i$Expanding the left side: $(2x + 3y) + i(-3x + 2y) = 4 + i$Equating real and imaginary parts:$2x + 3y = 4

Vedclass · Accepted Answer

$x = \frac{5}{13}, y = \frac{14}{13}$

Vedclass · Answer

(C) Given equation: $(x + iy)(2 - 3i) = 4 + i$Expanding the left side: $(2x + 3y) + i(-3x + 2y) = 4 + i$Equating real and imaginary parts:$2x + 3y = 4$ ... $(i)$$-3x + 2y = 1$ ... $(ii)$Multiplying $(i)$ by $3$ and $(ii)$ by $2$:$6x + 9y = 12$$-6x + 4y = 2$Adding the two equations: $13y = 14 \implies y = \frac{14}{13}$Substituting $y$ in $(i)$: $2x + 3(\frac{14}{13}) = 4 \implies 2x = 4 - \frac{42}{13} = \frac{52 - 42}{13} = \frac{10}{13} \implies x = \frac{5}{13}$Thus,$x = \frac{5}{13}$ and $y = \frac{14}{13}$.

The real values of $x$ and $y$ for which the equation $(x + iy)(2 - 3i) = 4 + i$ is satisfied,are

Similar Questions

If $(1 - i)x + (1 + i)y = 1 - 3i$,then $(x, y) = $

Express $(5-3i)^{3}$ in the form $a+ib$.

By simplifying $i^{18}-3i^7+i^2(1+i^4)(i)^{22}$,we get

Express the given complex number in the form $a+ib$: $\left(-2-\frac{1}{3}i\right)^{3}$

${\left( \frac{1 + i}{1 - i} \right)^2} + {\left( \frac{1 - i}{1 + i} \right)^2}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module