How are complex fractions simplified? Present an example of a simplifying a complex fraction.?

Alright.

Problem:
-3 + 4i / 2 + i

Solution:
(-3+4i)(2-i) / (2+i)(2-i)

(6 + 8i + 3i - 4i^2) / (4 + 2i - 2i - i^2)

(10 + 11i) / 5

2 + (11/5)i

DO NOT forget to separate the fraction because that is the WHOLE POINT of that entire procedure, to get a+bi.

They are simplified by "rationalizing" the denominator...I use quotes because usually rationalizing is use to refer to taking out square roots...but it's the same idea.

You may have seen this with square roots:

1/(1 + sqrt(2))

Multiply by conjugate:

(1 - sqrt(2)) / (1 + 2) = (1 - sqrt(2))/3

The conjugate works because of differences of squares:

(x + y) * (x - y) = x^2 - y^2

So comlex numbers work the same way:

You can "rationalize" the complex number by multiplying by it's complex conjugate (just negate the imaginary part):

(a + bi) * (a - bi) = a^2 - (ib)^2 = a^2 - (i^2)(b^2) = a^2 - (-1)b^2 = a^2 + b^2

So...that's how you get rid of the imaginary part in the denominator...someone else already gave you an example.