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**renjer****Member**- Registered: 2006-04-29
- Posts: 50

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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**renjer****Member**- Registered: 2006-04-29
- Posts: 50

Anyone pls help?

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

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

Thats the answer I got.

*We need to have 2*x* to be in the fourth quadrant because cos(2*x*) must be positive and sin(2*x*) negative in order for the solution to work. (And cos(4*x*) is already known to be negative.))

*Last edited by JaneFairfax (2007-05-26 00:42:55)*

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

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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