Question

multiplying complex numbers quiz
started: jan 9 at 7:34am
quiz instructions
question 1
$i^3 = $
1
$i$
-1
-$i$

Explanation:

Step1: Recall the definition of \(i\)

We know that the imaginary unit \(i\) is defined as \(i = \sqrt{-1}\), so \(i^{2}=(\sqrt{-1})^{2}=- 1\).

Step2: Calculate \(i^{3}\)

Using the property of exponents \(a^{m + n}=a^{m}\times a^{n}\), we can write \(i^{3}=i^{2}\times i\).
Substitute \(i^{2}=-1\) into the above formula, we get \(i^{3}=-1\times i=-i\).

Answer:

\(-i\) (corresponding to the option with \(-i\))