Question

Simplify the given expression below 2 over 2+5i

Answer 1

First, we can write this as a fraction:
2/(2+5i)
Then, we need to rationalize the fraction. This means that i is not present in the bottom of the fraction. To do this, we can multiply the numerator and denominator by (2-5i). This is because when multiplied by the numerator, a quadratic will be created when i is squared to create negative 1, and the other terms with i cancel each other out. You will see this in a moment.
2(2-5i)/(2+5i)(2-5i)
Then, distribute. Make sure to FOIL the bottom. This gives you:
(4-10i)/(4+10i-10i-25i^2)
The terms 10i and -10i cancel each other out, leaving us with:
(4-10i)/(4-25i^2)
Since i is the square root of negative 1, squaring it will give us -1. Thus, we have:
(4-10i)/(4+25)
And simplifying further:
(4-10i)/29
Sometimes, you are asked to write it in a+bi form, meaning you split it into two fractions. It looks like this:
(4/29) - ((10i)/29), or (4/29) - (10/29)i