Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

## #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.

Offline

## #2 2007-05-25 01:09:14

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

Anyone pls help?

Offline

## #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)

Offline

## #4 2007-05-26 00:19:09

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

### Re: Complex Numbers

*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)

Offline

## #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.
­

Offline