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# Complex number---pure 4 watch

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1. Anyone knows how to do it?
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2. |w| = 5, so w must be either 5, -5, 5i, -5i, 3+4i, 3-4i, -3+4i, -3-4i.

Try each case since there are so few to choose from.
3. (Original post by JamesF)
|w| = 5, so w must be either 5, -5, 5i, -5i, 3+4i, 3-4i, -3+4i, -3-4i.

Try each case since there are so few to choose from.
Sorry, I dont understand.
Can you show me how to do it?
4. (Original post by superkillball)
Anyone knows how to do it?
Let w = x + iy

For the first one w = 4 - 3i
5. (Original post by JamesF)
|w| = 5, so w must be either 5, -5, 5i, -5i, 3+4i, 3-4i, -3+4i, -3-4i.

Try each case since there are so few to choose from.
Thats only true if the coefficients are integers - in fact there are infinitely many solutions given by the circle in the complex plane radius 5, centre origin
6. (Original post by It'sPhil...)
Let w = x + iy

For the first one w = 4 - 3i
How come w= 4 - 3i?
7. (Original post by superkillball)
How come w= 4 - 3i?
let w = x + iy
since lwl = 5, x^2 + y^2 = 25
so we have l 12 - 9i + x + iyl = 15 + 5 = 20
so (12 + x)^2 + (y - 9)^2 = 400
expand and sub x^2 = 25 - y^2
24x - 18y = 150
=> x = (75 + 9y)/12
sub into x^2 + y^2 = 25
ie (after cancelling) y^2 + 6y + 9 = 0
=> (y + 3)^2 = 0
y = -3 x = 4

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