# How do you prove a multiplicative inverse of a complex number?

## How do you prove a multiplicative inverse of a complex number?

Explanation: Multiplicative inverse of a number system is also called reciprocal. Multiplicative identity in a number system is a number, which when multiplied by number, say x , returns the number itseIf. This number is 1 and while dealing with complex numbers, it is 1+i0 .

### What is the multiplicative inverse of the complex number 1 i?

The multiplicative inverse of 1+i is 1/1+i.

What is the multiplicative inverse of a complex number z?

Hence the multiplicative inverse of z is. =∣z∣

How do you find the inverse of a complex number?

Quick Reference. If z is a non-zero complex number and z=x+yi, the (multiplicative) inverse of z, denoted by z −1 or 1/z, is When z is written in polar form, so that z=reiθ=r (cos θ+i sin θ), where r ≠ 0, the inverse of z is (1/r)e −iθ=(1/r)(cos θ−i sin θ).

## What is the multiplicative inverse of 3i?

The multiplicative inverse of 3i is −i3 .

### What is the multiplicative inverse of 1 3?

Answer: The answer is of course one third, or 1/3, since: 3 * 1/3 = 1.

What is the multiplicative inverse of 2?

1/2
The multiplicative inverse of any number is another number which when multiplied by the original number gives the product as 1. For example, the multiplicative inverse of 2 is 1/2. It is also known as the reciprocal of a number.

What is the multiplicative inverse of 4?

The multiplicative inverse of 4 is 1/4. (One-fourth is 1/4 in written form.)

## What is the multiplicative inverse of 4 7i?

i.e, multiplicative inverse of 4/7 is 7/4.

### How do you find the multiplicative inverse?

The multiplicative inverse of a fraction a/b is b/a. For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4.

What is the multiplicative inverse of 5?

1/5
For example, the multiplicative inverse of 5 is 1/5.

What is the multiplicative inverse of 5 /- 3?

Answer. Answer: multiplicative inverse means the reciprocal of a given fraction. so here the fraction is 5/3 and its reciprocal is 3/5 which is the multiplicative inverse of 5/3.