QUICK HELP complex numbers

  • Thread starter aisha
  • Start date
  • #1
584
0
Let Z1 = 3-i
Z2=7+2i express (1/Z1)-(1/Z2) in form a+bi
SOMEONE plzzzzzzz HELP ME!!! I dont have a clue as to how to do this :cry:
What do I do?
Where do I start? :cry:
 

Answers and Replies

  • #2
Have you ever rationalized the denominator of a fraction before? This is pretty much the same thing. For instance, when you have a fraction such as [tex]\frac{5}{\sqrt{3}+2}[/tex], you multiply the top and bottom by the conjugate, because you know a difference of squares will result in a rational number, because the square root of a rational squared is a rational. The same idea applies here: just keep in mind that [tex]i=\sqrt{-1}[/tex], and apply the same concept.

Hope that helps! :)
 
  • #3
299
0
Do you know what a "complex conjugate" is?
 
  • #4
584
0
Parth Dave said:
Do you know what a "complex conjugate" is?

Yes I do it is the opposite sign well when dividing you take the denominator and divide by the conjugate I know that but in this question I dont know what to do or what order to do it in plz help me plzzz
 
  • #5
BobG
Science Advisor
Homework Helper
223
84
nolachrymose said:
Have you ever rationalized the denominator of a fraction before? This is pretty much the same thing. For instance, when you have a fraction such as [tex]\frac{5}{\sqrt{3}+2}[/tex], you multiply the top and bottom by the conjugate, because you know a difference of squares will result in a rational number, because the square root of a rational squared is a rational. The same idea applies here: just keep in mind that [tex]i=\sqrt{-1}[/tex], and apply the same concept.

Hope that helps! :)
nolachrymose described it pretty well.

If you substituted i for the square root of 3,

[tex]\frac{5}{\sqrt{-1}+2}[/tex],

and multiplied by the conjugate, you'd get:

[tex]\frac{5(\sqrt{-1}-2)}{-1 - 4} = 2 - \sqrt{-1}[/tex]

The i is square root of negative one. If you have 3i and square it, you get -9. Other than keeping the negative signs straight, it's just like working with a square root.
 
  • #6
584
0
Ive never rationalized the denominator of a fraction :frown: so im a little lost I tried multiplying 1/3-i first by the conjugate and got the answer of 3+i/10 and then i did the same for z2 and got 7-2i/53 but if i subtract the two i dont get the right answer plz show me how do i divide first subtract use conjugates or what?
 
  • #7
299
0
As far as I can tell you rationalized the two properly. Unless you made a subtraction error, your answer should be right. What did you get as the final answer?
 
  • #8
584
0
There are 4 possible answers
a)89/24-73/24i

b)89/24+73/24i

c)-89/24+73/24i

d)89/24i-73/24

I dont get anything close to these when i take those two answers and subtract them. Please help me Ive been doing this one forever :mad:
 
  • #9
BobG
Science Advisor
Homework Helper
223
84
All of their choices are wrong.

So what did you get? Something close to

[tex]\frac{89+73i}{530}[/tex]
 
  • #10
BobG
Science Advisor
Homework Helper
223
84
I think I know where they made their mistake. You can do this two ways.

[tex]\frac{1}{3-i}-\frac{1}{7+2i}[/tex]

[tex]\frac{3+i}{9-(-1)}-\frac{7-2i}{49-(-4)}[/tex]

[tex]\frac{3+i}{10}-\frac{7-2i}{53}[/tex]

[tex]\frac{(159+53i)-(70-20i)}{530}[/tex]

[tex]\frac{89+73i}{530}[/tex]

Or:

[tex]\frac{1}{3-i}-\frac{1}{7+2i}[/tex]

[tex]\frac{7+2i}{(3-i)(7+2i)}-\frac{3-i}{(3-i)(7+2i)}[/tex]

[tex]\frac{7+2i-3+i}{(21-(-2))+(6i-7i)}[/tex]

[tex]\frac{4+3i}{23-i}[/tex]

[tex]\frac{(4+3i)(23+i)}{(23-i)(23+i)}[/tex]

[tex]\frac{(92+(-3))+(69i+4i)}{529-(-1)}[/tex] Here's where they made their mistake

[tex]\frac{89+73i}{530}[/tex]

You can break this up into two separate fractions, if you want:

[tex]\frac{89}{530}+\frac{73}{530}i[/tex]

Instead of multiplying (23-i)(23+i) and getting 529+1, they got 23+1. So, the answer they most likely picked is (b)
 
  • #11
arildno
Science Advisor
Homework Helper
Gold Member
Dearly Missed
10,025
134
A great example of why multiple choice exams are (IMO) inferior to some other exam types which are less sensitive to designer flaws.
 
  • #12
BobG
Science Advisor
Homework Helper
223
84
arildno said:
A great example of why multiple choice exams are (IMO) inferior to some other exam types which are less sensitive to designer flaws.
A flaw?! Or is it really a hidden 'feature'? :devil: (how come we don't have a 'shifty eyed' smilie?)

"B's for everyone who answers all the questions right. A's for everyone who catches my error and figures out exactly where I made my mistake!"
 
  • #13
584
0
BobG said:
All of their choices are wrong.

So what did you get? Something close to

[tex]\frac{89+73i}{530}[/tex]

Well my answer was (89-33i)/530
u are right that the question that was correct was b with the error in it. I think our answers are different because when u expanded -10(7-2i)/530 u wrote -70-20i shouldnt this be -70+2i because of the two negative signs? I will for sure point this question out to my teacher maybe she will give me an "A" lol for cathching the errors. Thanks so much I thought I was doing this totally wrong, but I guess not thanks again ur my HERO :smile:
 

Related Threads on QUICK HELP complex numbers

  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
2
Views
777
  • Last Post
Replies
8
Views
2K
S
  • Last Post
Replies
2
Views
2K
Replies
1
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
2
Replies
27
Views
2K
  • Last Post
Replies
17
Views
3K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
1K
Top