Trigonometry_ Ice Cream life: The Late BLOG :'(

Aim : How do we use complex conjugates to divide imaginary numbers?

So ... we are on a brand new math journey ....

when dealing with imaginary numbers,things can get a bit complex.

For example we can get a question like =
Express your answer in a, a+ bi form :

3-4i
3+i

We know,from our previous knowledge that an i in the denominator wont satisfy the answer because it does not provide a real answer. To correctly answer this question we need to use the conjugate.

A conjugate, is the opposite of the expression.If the expression has a positive sign we switch it to a negative sign to make it a conjugate.

For Example:
Initial expression:    Conjugated expression:
24+i 24-i
30- i 30+i

MOVING ON TO THE FIRST EXAMPLE~

Express your answer in a, a+bi form:
3-4i
3+i

STEP 1: Find the conjugate of the denominator and multiply it to the top and bottom of the expression.

3-4i = (3-4i)(3-i)
3+i = ( 3+i)(3-i)

STEP 2: Distribute the expressions. (try to do one part at a time )

(3-4i)(3-i) = 9-3i-12i+4i2 (remember the imaginary numbers rule)
= 9-15i+4(-1)
= 9-15i -4    (combine like terms)
= 5-15i

(3+i)(3-i) = 9-3i+3i-i2
  = 9-i2 (imaginary number rule)
= 9-(-1)   (a negative number multiplied by a negative number produces a positive number)
=9+10
= 19
Step 3: Combine both answers of the both to have a final answer.

TA-DA YOUR ANSWER:

5-15i

your answer could be shown this way as well as :

5 - 15i

19 19

Now YOU try it out :)