Chapter A.7, Problem 46AYU

To determine

To write: The given expression in the standard form $a+ib$ .

Answer to Problem 46AYU

The given expression in the standard form $a+ib$ is $0$ .

Explanation of Solution

Given information:

The expression is $i^7+i^5+i^3+i$ .

Calculation:

Consider the expression.

  $\begin{array}{c}{i}^7+i^5+i^3+i=i^4{i}^3+i^3{i}^2+i^3+i\\ =1\left(-i\right)+\left(-i\right)\left(-1\right)+\left(-i\right)+i\\ =-i+i-i+i\\ =0\end{array}$