Simplify the given expression below: 2 divided by the quantity of 2 plus 5i.

Solution:

Given, 2/2 + 5i

Simplify to get rid of complex terms from the denominator.

Multiply and divide by 2 - 5i.

=2(2-5i)/(2+5i)(2-5i)

Using the distributive property

=2(2 - 5i)/4 - 10i + 10i - 25i²

=2(2 - 5i)/4 - 25i²

We know that i² = -1

= 2(2 - 5i)/4 + 25

= 2(2 - 5i)/29

= 4/29 - 10i/29.

Therefore, the simplified expression is 4/29 - 10i/29.

Simplify the given expression below: 2 divided by the quantity of 2 plus 5i.

Summary:

Simplifying the given expression below, 2 divided by the quantity of 2 plus 5i, we get 4/29 - 10i/29.