Question

question 1 of 10
what is $(-i)^3$?

a. 1

b. -1

c. -i

d. i

Explanation:

Step1: Recall the property of imaginary unit \(i\)

We know that \(i^2 = -1\), and we need to calculate \((-i)^3\). First, expand \((-i)^3\) using the exponent rule \((ab)^n = a^n b^n\), so \((-i)^3 = (-1)^3\times i^3\).

Step2: Calculate \((-1)^3\) and \(i^3\)

Calculate \((-1)^3\): \((-1)^3=-1\) (since \((-1)\times(-1)\times(-1)= -1\)).
Calculate \(i^3\): \(i^3 = i^2\times i\), and since \(i^2 = -1\), then \(i^3=-1\times i=-i\).

Step3: Multiply the results

Now, multiply \((-1)^3\) and \(i^3\) together: \((-1)^3\times i^3=-1\times(-i)=i\).

Answer:

D. \(i\)