Question:
Find the multiplicative inverse of $2 - 3i$.
Find the multiplicative inverse of $2 - 3i$.
Updated On: Jul 6, 2022
- $2/13+i(3/13)$
- $2/13-i(3/13)$
- $2+3i$
- None of these
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The Correct Option is A
Solution and Explanation
Let $z = 2-3i$ , then, $z^{-1}=\frac{1}{2-3i}$
$=\frac{2+3i}{\left(2-3i\right)\left(2+3i\right)}$
$=\frac{2+3i}{2^{2}-\left(3i\right)^{2}}$
$=\frac{2+3i}{13}$
$=\frac{2}{13}+\frac{3}{13} i$
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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.
