2016-09-26 09:23:06
Simplify the given expression below 2 over 2+5i
2016-09-26 16:04:06

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