Checkpoint: The Imaginary Unit 𝑖 Solution

Checkpoint: The Imaginary Unit 𝒊 Solution

Evaluate.

$18 \div 4 = 4 R 2 {(i^{4})}^{4} \cdot i^{2} - 1$

Note

Q: By what number do you divide the exponent to simplify the imaginary unit? Explain.

A: 4, because $i^{4} = 1$

$43 \div 4 = 10 R 3 {(i^{4})}^{10} \cdot i^{3} - i$

Note

Q: Why is it important to know the remainder when the number i is raised to a power?
A: Because this determines the value –1, –i, or i.