In analytical geometry, there are two types of roots: real roots and complex roots. Imaginary roots are those with the term 'i'. These are complex numbers that can be found on the number line, thus they are called imaginary. The term 'i' is equal to the expression √(-1). So when you solve these equations, just treat the complex numbers as is they are variables.
The only way to solve these is to test each choice such that its final answer would be 4i. These are important equivalents to know:
sin 0° = 0 cos 0° =1
sin 90° =1 cos 90° =0
sin 180° =0 cos 180° = -1
sin 270° = -1 cos 270° = 0
Using these values, let's simplify each choise.
A. 4(1 + i (0)) = 4
B. 4(0 + i (-1)) = -4i
C. 4(0 + i (1)) = 4i
D. 4((-1) + i (0)) = -4
The answer is C.
