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# FP1 Complex Number Maths Question watch

1. z = a+bi
z^2 = c+di

prove that a^2=1/2(c+sqrt(c^2+d^2))
2. (Original post by intesar)
z = a+bi
z^2 = c+di

prove that a^2=1/2(c+sqrt(c^2+d^2))
As z=a+bi, it follows that .

But you also know that

So you two expressions which are equal to . Equate them and make the subject.
3. you need to equate the real parts and then the imaginary parts of ( a + bi )2 and c + di

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