# Complex Numbers-basic operations

• Jul 25th 2009, 10:37 PM
Awsom Guy
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.
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
• Jul 25th 2009, 11:14 PM
songoku
You left out the denominator in your work
• Jul 25th 2009, 11:17 PM
Awsom Guy
No change
well I didn't put it in because it is a one and it doesn't change anything....
• Jul 25th 2009, 11:21 PM
songoku
It's 2
• Jul 26th 2009, 03:05 AM
HallsofIvy
Quote:

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)?

Quote:

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.