Question

Which expression represents the number
`5i^(4)`+
`2i^(3)` +
`8ix^(2)` +
`\sqrt -4` rewritten in a+bi form?

Please help me out!

Which is the answer?

−3+2i
5+0i
5−2i
​−3−4i
−3+0i

Answer 1

Explanation:

Recall the following identities:

i^4 = 1

i³ = -i

i² = -1

i = 1

Thus, the first term, 5i^4, is equivalent to 5.

The second term, 2i³, is equivalent to -2i.

The third term, 8ix², is equivalent to 8ix².

The fourth term, √(-4), is equivalent to 2i.

Combining these four results, we get:

5 - 2i + 8ix² + 2i

-2i and 2i cancel out, leaving 5 + 8ix²