# Thread: Complex Numbers-basic operations

1. ## Complex Numbers-basic operations

I think this goes in this section but anyway...

Simplify..
-3-i/1+i + 1+3i/1-i
I hope this makes sense.
The answer is -3+3i
This is my working but I can't get the answer..
-3-i/1+i * 1-i/1-i
(-3-i)(1-i)
-3(1-i)-i(1-i)
-3+3i-i-1
-4+2i
Then....
1+3i/1-i * 1+i/1+i
(1+3i)(1+i)
(1+3i)(1+i)
1(1+i)+3i(1+i)
1+i+3i-3
-2+4i
Finally..
-4+2i-2+4i
-6+6i

This is my working but I cannot get the right answer....
Thanks

2. You left out the denominator in your work

3. ## No change

well I didn't put it in because it is a one and it doesn't change anything....

4. It's 2

5. Originally Posted by Awsom Guy
I think this goes in this section but anyway...

Simplify..
-3-i/1+i + 1+3i/1-i
I hope this makes sense.
No, it doesn't because you have left out parentheses. Do you mean
(-3-i)/(1+i)+ (1+3)/(1-i)?

The answer is -3+3i
This is my working but I can't get the answer..
-3-i/1+i * 1-i/1-i
(-3-i)(1-i)
-3(1-i)-i(1-i)
-3+3i-i-1
-4+2i
Then....
1+3i/1-i * 1+i/1+i
(1+3i)(1+i)
(1+3i)(1+i)
1(1+i)+3i(1+i)
1+i+3i-3
-2+4i
Finally..
-4+2i-2+4i
-6+6i

This is my working but I cannot get the right answer....
Thanks
You've written things in a very confused way!

Simplify (-3-i)/(1+i) by 'rationalizing' the denominator: (-3-i)(1-i)/(1+i)(1-i)= (-4+ 2i)/2= -2+ i.

Simplify (1+3i)/(1-i) by 'rationalizing' the denominator: (1+3i)(1+i)/(1-i)(1+i)= (-2+ 4i)/2= -1+ 2i.

The sum is -3+ 3i.

Your attempt to do things the "easy way" is what messed you up.