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# some questions on complex numbers help fast please

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1. Compute $i+i^2+i^3+\cdots+i^{2016}+i^{2017}$.

2. Find a complex number $z$ such that the real part and imaginary part of $z$ are both integers, and such that$$z\overline z = 89.$$

3. Simplify $(1+i)^{2016}-(1-i)^{2016}$.

4. Express $\frac 1{1+\frac 1{1-\frac 1{1+i}}}$ in the form $a+bi$, where $a$ and $b$ are real numbers.

Sep 8, 2021

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1. $i + i^2 + i^3 + \dots + i^{2016} + i^{2017} = -1$.

2. $z = 6 + 7i$ works.

Sep 9, 2021
#2
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One post = one question

This question has been closed.

Sep 9, 2021