Simplify 2i to the 5th power?
(2i)^5 = 2^5 * i^4 * i
= 32 (-1)^2 * i = 32 i
To simplify (2i)^5, we can use the rules of exponentiation.
First, we expand (2i)^5 as (2i)(2i)(2i)(2i)(2i).
Then, we can apply the rule (ab)^n = a^n * b^n to each term.
In this case, (2i)^5 simplifies to 2^5 * i^5.
Next, we simplify the terms. 2^5 equals 32, and i^5 can be rewritten as i^4 * i.
Since i^4 is equal to (-1)^2 (which equals 1), we have 32 * 1 * i.
Finally, since multiplying by 1 does not change the value, we have 32 * i, which simplifies to 32i.
Therefore, (2i)^5 simplifies to 32i.