Question:
If $(x+iy) (2-3i)=4+i$, then values of $x$, $y$ are
If $(x+iy) (2-3i)=4+i$, then values of $x$, $y$ are
Updated On: Jul 6, 2022
- $1$, $3/13$
- $2$ , $5/13$
- $\frac{5}{13}$ , $\frac{14}{13}$
- $0$ , $2$
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The Correct Option is C
Solution and Explanation
$\left(x+iy\right)\left(2-3i\right)=4+i$
$\Rightarrow\, 2x+3y+i\left(-3x+2y\right)=4+i$
Equating real and imaginary parts, we get
$2x+3y=4$ ,
$-3x+2y=1$
Solving these, we get $x=\frac{5}{13}$ ,
$y=\frac{14}{13}$
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Concepts Used:
Complex Numbers and Quadratic Equations
Complex Number: Any number that is formed as a+ib is called a complex number. For example: 9+3i,7+8i are complex numbers. Here i = -1. With this we can say that i² = 1. So, for every equation which does not have a real solution we can use i = -1.
Quadratic equation: A polynomial that has two roots or is of the degree 2 is called a quadratic equation. The general form of a quadratic equation is y=ax²+bx+c. Here a≠0, b and c are the real numbers.
