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FP1 Complex Number Maths Question

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

prove that a^2=1/2(c+sqrt(c^2+d^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 z2=(a+bi)2z^2=(a+bi)^2.

But you also know that z2=c+diz^2=c+di

So you two expressions which are equal to z2z^2. Equate them and make a2a^2 the subject.
you need to equate the real parts and then the imaginary parts of ( a + bi )2 and c + di

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