Question

2. If ¡2x+3 = i, where i = V-1, then which of the
following is a solution for x?
(1) x = 16
(3) x = 11
(2) x = 10
(4) x = 14

Answer 1

I assume you mean the equation

[tex]i^{2x+3} = i[/tex]

Since i = √(-1), we have i⁴ = 1 and so i⁵ = i. Then 2x + 3 must be some multiple of 5.

Now just check for which of the given choices that this holds:

x = 16 ⇒ 2x + 3 = 35 (yes)

x = 11 ⇒ 2x + 3 = 25 (yes)

x = 10 ⇒ 2x + 3 = 23 (no)

x = 14 ⇒ 2x + 3 = 31 (no)