Sebastian M. answered • 10/08/20

Experienced HS/College Tutor for Math and Standardized Tests

Note that the definition of i is that it is the number such that i=√-1. This means that i^{2}=-1. Squaring both sides means i^{4}=1. Multiplying both sides by i then implies i^{5}=i.

So to figure out (-i)^5 first notice that

-i = -1*i

=> (-i)^{5} = (-1*i)^{5} = (-1)^{5} * (i)^5

Here you should notice that -1 to an odd exponent is always -1 and i^{5}=i. So

(-1)^5 * (i^5) = -1*i = -i

So finally 2+(-i)^5 = 2+(-i) which is not a real number. The answer is false.