Multiplicative Inverse of Complex Numbers
The multiplicative inverse of a complex number a + bi, where a and b are real numbers and i is the imaginary unit (i2 = -1), is given by (a + bi)-1 or 1/ (a + bi).
To find the multiplicative inverse, you often multiply the numerator and denominator by the conjugate of the complex number. The conjugate of a + bi is a − bi. So, the multiplicative inverse becomes 1/ (a + bi) × (a-bi)/ (a + bi) = (a-bi)/ (a2 + b2).
Following are the examples of Multiplicative Inverse of Complex Numbers:
- Multiplicative inverse of 2 + 3i will be 1/ (2 + 3i) × (2 – 3i) / (2 – 3i) = 2-3i/13.
- Multiplicative inverse of -1 + 2i will be 1/ (-1 + 2i) × (-1-2i)/(-1-2i) = -1-2i/5.
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Multiplicative Inverse
Multiplicative inverse of a number is another number that, when multiplied by the original number, results in the identity element for multiplication, which is 1. In other words, for a non-zero number a, its multiplicative inverse is denoted as a−1, and it satisfies the equation: a⋅a-1 = 1. We can also define multiplicative inverse as the reciprocal of a number. A number when multiplied with its own multiplicative inverse(reciprocal), then we get 1. In this article, we will learn about multiplicative inverse their definition, multiplicative inverse of natural numbers, fraction, unit fraction, mixed fraction, and complex numbers.
Table of Content
- What is Multiplicative Inverse?
- Multiplicative Inverse of Natural Number
- Multiplicative Inverse of Fraction
- Multiplicative inverse of Mixed Fraction
- Multiplicative Inverse of Complex Numbers