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FP1 complex numbers

I need help for part b)

I understand why one of the roots is 2-i, but how do they know the other is -2+i? I really can't see it. thanks

Reply 1

ttoby

Here's a general rule that's useful to know:

Suppose c and b are complex numbers.

If

c^2 = b

then

(-c)^2 = (-1)^2 c^2 = c^2 = b

So if c is a square root of b then so is -c.

Reply 2

TenOfThem

Original post by syNK

I understand why one of the roots is 2-i, but how do they know the other is -2+i? I really can't see it. thanks

(a-b)^2 = (b-a)^2

Reply 3

ghostwalker

You can also consider it from the point of view of roots of polynomials.

If z^2=c, then the sum of the roots is 0, and so one root is minus the other.

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