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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
Member
Registered: 2006-04-29
Posts: 50

Re: Complex Numbers

Anyone pls help?

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#3 2007-05-25 22:28:24

JaneFairfax
Member
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
Member
Registered: 2007-02-23
Posts: 6,868

Re: Complex Numbers

That’s 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
Member
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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