Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Join our platform to connect with experts ready to provide detailed answers to your questions in various areas. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

If [tex]\( i = \sqrt{-1} \)[/tex], what is the value of [tex]\( i^3 \)[/tex]?

A. [tex]\(-1\)[/tex]
B. [tex]\(i\)[/tex]
C. [tex]\(1\)[/tex]
D. [tex]\(-i\)[/tex]


Sagot :

To solve for [tex]\( i^3 \)[/tex] where [tex]\( i = \sqrt{-1} \)[/tex]:

1. Start by knowing the fundamental property of [tex]\( i \)[/tex], which is:
[tex]\[ i = \sqrt{-1} \][/tex]

2. Next, calculate [tex]\( i^2 \)[/tex]:
[tex]\[ i^2 = (\sqrt{-1})^2 = -1 \][/tex]

3. Now, use the value of [tex]\( i^2 \)[/tex] to find [tex]\( i^3 \)[/tex]:
[tex]\[ i^3 = i \cdot i^2 \][/tex]

4. Substitute [tex]\( i^2 \)[/tex] with [tex]\(-1\)[/tex]:
[tex]\[ i^3 = i \cdot (-1) = -i \][/tex]

So, the value of [tex]\( i^3 \)[/tex] is:
[tex]\[ -i \][/tex]

Therefore, [tex]\( i^3 \)[/tex] evaluates to [tex]\(-i\)[/tex]. Among the given choices, the correct answer is:
[tex]\[ \boxed{-i} \][/tex]