A number $z=x+iy$, where $x,y\in\mathbb{R}$ and $i^2=-1$, is called a complex number. Its

Question

A number $z=x+iy$, where $x,y\in\mathbb{R}$ and $i^2=-1$, is called a complex number. Its real and imaginary parts are $\operatorname{Re}z=x$ and $\operatorname{Im}z=y$. Simplify each of the following complex numbers and state its real and imaginary parts. ${{\mathbf{i}}^{3}}$ ${{\mathbf{i}}^{4}}$ ${{\mathbf{i}}^{5}}$

Accepted Answer

(a) $-i$: real part $0$, imaginary part $-1$. (b) $1$: real part $1$, imaginary part $0$. (c) $i$: real part $0$, imaginary part $1$.

Complex Numbers - Introduction to Complex Numbers

Complex Numbers - Introduction to Complex Numbers

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