Attitude for solving $\int_{|z+1|=1} \frac{1}{z^{3}-i} d z$

Question

I am asked to calculate $$\int_{|z+1|=1} \frac{1}{z^{3}-i} d z$$ I was thinking to apply the Cauchy integral theorem but I am not sure how to express the set $|z+1|=1$ as a boundary of a disk in $\mathbb{C}$ can I write it as $D_1(-1)$? something make me feel uncomfortable with the minus sign.

Answer 1

$$|z+1| = 1$$ is the circle of radius $1$ centered at $-1+0\mathrm{i}$. One can write this circle as $-1 + 1\cdot \mathrm{e}^{\mathrm{i}\theta}$ allowing $0 \leq \theta \leq 2 \pi$ (or some translate of that interval).

More generally, $$|z-a| = b$$ is the circle of radius $b$ centered at $a$. One can write this circle as $a + b\cdot \mathrm{e}^{\mathrm{i}\theta}$ allowing $0 \leq \theta \leq 2 \pi$ (or some translate of that interval).