Multiplicative inverse of a complex number.
The multiplicative inverse (also known as the reciprocal) of a complex number is a number that, when multiplied by the original number, results in a product of 1. In other words, if z is a complex number, then its multiplicative inverse is 1/z, such that z * (1/z) = 1.
Here are five examples of the multiplicative inverse of a complex number:
Example 01:
The reciprocal of the complex number a + bi is 1/(a + bi) = a/(a^2 + b^2) - bi/(a^2 + b^2)
Example 02:
The reciprocal of 2 + 3i is 1/(2 + 3i) = 2/(2^2 + 3^2) - 3i/(2^2 + 3^2) = 0.36 - 0.48i
Example 03:
The reciprocal of -4 + 2i is 1/(-4 + 2i) = -4/(-4^2 + 2^2) + 2i/(-4^2 + 2^2) = -0.6 + 0.8i
Example 04:
The reciprocal of 1 - i is 1/(1 - i) = 1/(1^2 + (-1)^2) - i/(1^2 + (-1)^2) = 0.5 + 0.5i
Example 05:
The reciprocal of 0 + 5i is 1/(0 + 5i) = 0/(0^2 + 5^2) + 5i/(0^2 + 5^2) = 0 + 0.2i