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# Need help with imaginary number simultaneous equation

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1. Please help solve this it's bugging me a lot

z^2 - w^2 = -2+16i
z + iw = 4+4i

Thanks
2. (Original post by FlyingPooMan)

z^2 - w^2 = -2+16i
z + iw = 4+4i

Thanks
Find w in terms of z or z in terms of w in second equation, then sub that expression into the first equation.
3. (Original post by B_9710)
Find w in terms of z or z in terms of w in second equation, then sub that expression into the first equation.
I have tried both and cannot end up with the right answer. I got to z^2 -4z +1 = 4zi -8i
But I need z in the form of a+bi
4. (Original post by FlyingPooMan)
I have tried both and cannot end up with the right answer. I got to z^2 -4z +1 = 4zi -8i
But I need z in the form of a+bi
You can rearrange that to get the quadratic z^2 - (4+4i)z + (1+8i) = 0
You can now complete the square, or use the quadratic formula, to find z, where a=1, b=-(4+4i) and c=(1+8i)
5. (Original post by ejteb)
You can rearrange that to get the quadratic z^2 - (4+4i)z + (1+8i) = 0
You can now complete the square, or use the quadratic formula, to find z, where a=1, b=-(4+4i) and c=(1+8i)
Thanks man!! I got the right answer it was really clever how you arranged them in quadratic form

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