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#1 2007-05-23 00:12:09
- renjer
- Member
- Registered: 2006-04-29
- Posts: 50
Complex Numbers
cos (2z) = 1 + i
where z = x + yi
Find all solutions for z.
I really can't solve this, pls help.
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#2 2007-05-25 01:09:14
- renjer
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- Registered: 2006-04-29
- Posts: 50
Re: Complex Numbers
Anyone pls help?
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#3 2007-05-25 22:28:24
- JaneFairfax
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- Registered: 2007-02-23
- Posts: 6,868
Re: Complex Numbers
I can only think of using the formulae
Now try and solve these for x and y (if you can).
Last edited by JaneFairfax (2007-05-25 22:29:13)
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#4 2007-05-26 00:19:09
- JaneFairfax
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- Registered: 2007-02-23
- Posts: 6,868
Re: Complex Numbers
Thats the answer I got.
*We need to have 2x to be in the fourth quadrant because cos(2x) must be positive and sin(2x) negative in order for the solution to work. (And cos(4x) is already known to be negative.))
Last edited by JaneFairfax (2007-05-26 00:42:55)
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#5 2007-05-26 03:21:02
- JaneFairfax
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- Registered: 2007-02-23
- Posts: 6,868
Re: Complex Numbers
Oh, if you want all solutions, you can put
where the principal value of cos[sup]−1[/sup](2-√5) is in the range stated in my foregoing post.
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