Find the multiplicative inverse of the complex number \( 4 - 3i\)
Solution and Explanation
Let \(z=4-3i\)
Then,
\(z¯=4+3i\)
\(|z|^{2}=4^2+(-3)^2 =25\)
Therefore the multiplicative inverse of \(4-3i\)
\(z^{-1}=\dfrac{z¯}{|z|^{2}}\)
\(=\dfrac{4+3i}{25}\)
\(=\dfrac{4}{25}+\dfrac{3}{25}i\) (Ans.)
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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.
