# Thread: Simplifying complex numbers?

1. ## Simplifying complex numbers?

Can anyone show me how to simplify

2- square root 2i divided by 3+square root 6i

Now I used the conjugate 3- square root 6i

On the numerator I end up getting -6-2 square root 6- 3 square root 2i

On the denominator I end up getting 27

However I checked my answer and apparently I am wrong

What error could I have committed?

2. Originally Posted by homeylova223
Can anyone show me how to simplify
2- square root 2i divided by 3+square root 6i
Now I used the conjugate 3- square root 6i
On the numerator I end up getting -6-2 square root 6- 3 square root 2i
On the denominator I end up getting 27
The denominator should be 15. It is square of the absolute value of the denominator.

3. So would the conjugate be 3+square root 6i and multiply this to the denominator to get it squared?

4. Z = 3 + i \sqrt{6} when conjugated you get 3 - i \sqrt{6} ....

so denominator looks like 3^2 + 6 = 15

5. Originally Posted by homeylova223
So would the conjugate be 3+square root 6i and multiply this to the denominator to get it squared?
This is a of the most use formula.

6. I squared it

and I end up getting

9+3\sqrt{6i} + 3\sqrt{6i} + 36i^2

How do you get 15 as the denominator?

7. Originally Posted by homeylova223
Can anyone show me how to simplify

2- square root 2i divided by 3+square root 6i

Now I used the conjugate 3- square root 6i
I assume that by "used" you mean you multiplied both numerator and denominator by it. Okay, (2- i sqrt(2))(3- i sqrt(6))= 2(3)- 2(i sqrt(6))- (i sqrt(2)(3)+ i^2(sqrt(2)(sqrt(6)= 6- 2i sqrt(6)- 3i sqrt(2)- sqrt(12)- not at all what you have.
(3+ i sqrt(6))(3- i sqrt(6)= 9- i^2(sqrt(6))^2= 9+ 6= 15.

On the numerator I end up getting -6-2 square root 6- 3 square root 2i

On the denominator I end up getting 27

However I checked my answer and apparently I am wrong

What error could I have committed?
Since you don't show what you did- exactly how you multiplied, it is impossible to say. I do note that 27 = 36 - 9 so you might have squared 6 instead of sqrt(6)- but then I can't see why you would have subtracted.

8. Originally Posted by homeylova223
I squared it

and I end up getting

9+3\sqrt{6i} + 3\sqrt{6i} + 36i^2

How do you get 15 as the denominator?
Careful with the negative signs. The denominator is
$(3 + i \sqrt{6})(3 - i \sqrt{6}) = 9 + -3i \sqrt{6} + 3i \sqrt{6} - 6i^2$

-Dan