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# more complex numbers! watch

1. Sorry to keep posting questions but theres a few more things i'm not sure on so would appreciate any help.

1.Can z^2+i be factorised?
2.What is the complex conjugate of an equation z^2+az+b=0 where a and b are real?
3.How to show z1z2* is invariant under a rotation of z1 and z2 about the origin in an Argand diagram? (where z1 and z2 are different complex numbers)
4.Showing that [a+b]^2 + [a-b]^2 = 2([a]^2 + [b]^2) where a and b are complex numbers and how this is interpreted geometrically.

Thanks v much if you have any suggestions x
2. 1. yes :- [z + (i/√2 - 1/√2)][z - (i/√2 + 1/√2)]

2. z*² + az* + b = 0

3. do you know matrix/vector algebra? z1z2* is the dot product of two vectors z1 and z2 (where the components are the real and imaginary parts) and that is always invariant under rotation

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Updated: November 13, 2004
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