Respuesta :

tramserran

Answer:   [tex]\bold{\dfrac{3}{5}-\dfrac{1}{5}}i[/tex]

Step-by-step explanation:

Rationalize the denominator. Then separate into the a & b-components.

[tex]\dfrac{1+3i}{5i}\bigg(\dfrac{i}{i}\bigg)\quad =\quad \dfrac{i+3i^2}{5i^2}\quad =\quad \dfrac{i+3(-1)}{5(-1)}\quad =\quad \dfrac{i-3}{-5}\quad =\quad \dfrac{3-i}{5}\\\\\\=\large\boxed{\dfrac{3}{5}-\dfrac{1}{5}i}[/tex]

The result in the form of a + bi is [tex]\frac{3}{5}+(-\frac{1}{5} )i[/tex].

What is a complex number?

A complex number is any number that has "i" in it. The value of i is √-1. The root of -1 does not exist, and therefore it is an imaginary number.

We can evaluate the expression as shown below:

The expression is given as:

[tex]\frac{1+3i}{5i}[/tex]

This given expression has an imaginary number as its denominator. This should be removed. This can be removed by rationalizing the denominator.

We can rationalize the entire expression as shown below:

[tex]\frac{1+3i}{5i}=\frac{(1+3i)5i}{5i(5i)}\\= \frac{5i-15}{-25}\\=-\frac{i}{5} +\frac{3}{5}\\=\frac{3}{5}+(-\frac{1}{5} )i[/tex]

We have written the equation in the form of a + bi.

The equation written in a + bi form is [tex]\frac{3}{5}+(-\frac{1}{5} )i[/tex].

Therefore, we have found that the result in the form of a + bi is [tex]\frac{3}{5}+(-\frac{1}{5} )i[/tex].

Learn more about complex numbers here: https://brainly.com/question/16835201

#SPJ2

Otras preguntas