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#1 2008-12-13 20:48:26

ganesh
Moderator
Registered: 2005-06-28
Posts: 21,319

Complex Numbers - Pre University level I

1. What are the Real and Imaginary parts of the number 4 -i√3.

2. What is the conjugate of

?

3. If z=2 - i√3, then what is the value of

?

4. Express the following complex number in the forma + ib.

5. Find the real and imaginary parts of

.

6. If

,
find the conjugate of
.


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Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#2 2008-12-19 14:49:47

glenn101
Member
Registered: 2008-04-02
Posts: 108

Re: Complex Numbers - Pre University level I

1.
real part is 4
complex part is -i√3.
2.
the conjugate is
1/2+1/2*i
4.
5+5i   3+4i
------*------
3-4i    3+4i
= 15+20i+15i+20i^2
    --------
    25
= 15-20+20i+15i
   -------
   25
= -5+35i
   ------
    25
= -1   7
   ---+---*i
    5    5

Thats all I can do with my complex knowledge:)


"If your going through hell, keep going."

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#3 2008-12-19 22:45:57

ganesh
Moderator
Registered: 2005-06-28
Posts: 21,319

Re: Complex Numbers - Pre University level I

glenn101,
Your answers are all correct,
the only trivial mistake I noticed is in answer to 1, where when the real and imaginary parts are said, the imaginary part shouldn't include 'i'.
Well done!!! smile


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#4 2008-12-28 16:07:30

careless25
Real Member
Registered: 2008-07-24
Posts: 559

Re: Complex Numbers - Pre University level I

4. (-5 + 35i)/ 25

-0.2 + 1.4i

Edit: Oops!

Last edited by careless25 (2008-12-30 04:23:35)

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#5 2008-12-28 16:55:08

ganesh
Moderator
Registered: 2005-06-28
Posts: 21,319

Re: Complex Numbers - Pre University level I

A minor mistake, careless25. Please try and post the correct answer.


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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