Complex Numbers (Standard)

Complex Numbers: core idea

• 1. $(1+i)/(1-i)$: imaginary part?

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• 2. Roots of $z^2-2z+5=0$: real part?

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• 3. $|1+i|$?

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• 4. $(1+i)^4$?

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• 5. Locus $|z-1|=2$: radius?

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• 6. Cube roots of unity: sum?

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• 7. $z+\bar z=4$: Re$(z)$?

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• 8. $|z|^2$ for $z=3+4i$?

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• 9. De Moivre: $(\cos\theta+i\sin\theta)^2$ real part equals $\cos(k\theta)$ with $k=$?

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