## Questions and Answers

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- If $x = 2 + 3i$ and $y = 2 - 3i$, what is the value of $x^3 + y^3$?

Answer: $x^3 + y^3 = (2 + 3i)^3 + (2 - 3i)^3$

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- Express $5 + i$ in the form $2 + 3i$ ($\overline{z}^3$).

Answer: $5 + i = (2 + 3i)^3$

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- Express $1 + i\sqrt{3}$ in polar form.

Answer: $1 + i\sqrt{3} = r(\cos \theta + i\sin \theta)$

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- Find the modulus and argument of $1 + \cos \theta + i\sin \theta$.

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- Check the existence of $\lim_{z \to 0} (x^3 + y + i(x^2 - y^2))$.

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