Given that z=-2+i , express in the form of a+bi

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- May 20th 2009, 12:52 AMthereddevilscomplex number
Given that z=-2+i , express in the form of a+bi

- May 20th 2009, 01:26 AMmathsquest
Write -2 + i as x + i y ; r = (x^2 + y^2)^ (1/2)

Z = x + i y = r e^ i theta = r ( cos theta + i sin theta) from De Moivre;s

Theorem

where sin theta = y / (x^2 + y^2)^ (1/2) and

cos theta = x / (x^2 + y^2)^ (1/2)

Just substitute for Z + 1/Z and remember sin(-theta) = - sin theta. - May 20th 2009, 03:41 AMthereddevils
Is there a simpler way of doing this ?

This is what i tried :

and

i am not sure whether i am correct up to this step but after solving , i get weird values for a and b .. - May 21st 2009, 08:53 PMmathsquest
Actually the problem is because there are roots of a complex no involved I think and we have to involve the unit circle etc.

I tried it too . I got 4a^4 + 8a^2 - 1 = 0 . Put a^2 = x and then solve

4x^2 + 8 x - 1 = 0 to get x = -1 +or- 1/2 sqrt 5

Choose the +ve value and x = 0.118 or a = 0.3435 . Similarly try for b.

We have to ignore the value which is -ve else we end up with a being a complex no starting from the assumption it is not! - May 22nd 2009, 07:57 AMstapel
- May 22nd 2009, 08:13 PMmathsquest
You seem to have solved for Z + 1/Z and not Z + 1/sqrt Z

- May 25th 2009, 11:13 AMMath's-only-a-game