Simplify the given expression below: 4 divided by the quantity of 3 minus 2i

Solution:

Given, 4 divided by the quantity of 3 minus 2i is 4/(3 - 2i)

Let z = 4/(3 - 2i)

Here z denotes the complex number.

Now multiply and divide throughout by conjugate of the denominator, which is a number with the same real part and the opposite imaginary part to make the denominator real.

Conjugate in math means to write the negative of the second term.

By flipping the sign between two terms in a binomial, a conjugate in math is formed.

Here the conjugate is 3 + 2i

z = 4(3 + 2i)/ [(3 - 2i)(3 + 2i)]

= (12 + 8i)/13

= (12/13) + (8i/13)

Simplify the given expression below: 4 divided by the quantity of 3 minus 2i

Summary:

The given expression 4 divided by the quantity of 3 minus 2i = 4 / (3 - 2i), can be written as (12/13) + (8i/13).