imaginary number help?

Question

3 + 2i
--------
3 - 2i

look at it as a fraction. thanks in advance

Answer 1

Multiply the equation by 1... by multiplying both the top and bottom by the same value. That value being the conjugate of the denominator.

A conjugate of a complex number is the same real portion but it has the negative of the imaginary portion.
a + bi and a - bi are conjugates of one another.

The conjugate of the numerator is 3-2i and that of the denominator is 3+2i.

So, multiply both the top and the bottom by 3+2i

In the top, you are just squaring what is there already. In the bottom, the imaginary components cancel out

Answer 2

are you trying get a real number denominator? If so then multiply by the value of 1. Meaning:


(3 + 2i)/(3 + 2i).

That will give you

(9 + 6i - 4) / (9 + 4) which simplifies to

(5 + 6i) / 13

Answer 3

(3 + 2i) / (3 - 2i)

Multiply by (3 - 2i)

We get (9 - 4i^2) / (9 - 6i + 4i^2) like (a^2 - b^2) / (a - b)^2

= 9 + 4 / (9 - 6i - 4) (remember that i^2 = -1)

= 13 / ( 5 - 6i)

To simplify further, multiply the whole thing by (5 + 6i)

= 13 (5 + 6i) / (5^2 - 6i^2)

= (65 + 78i) / 11

Answer 4

Multiply the denominator and numerator by its conjugate (3+2i) and simplify.