how is this the right answer?..pls explain?

Question

For i = , if 3i (2 + 5i) = x + 6i, then x = ?
A. –15
B. 5
C. 5i
D. 15i
E. 27i

the answer is a

Answer 1

kay, complex variables ftw I'll explain it step by step

starting with 3i(2 + 5i) = x + 6i
you distribute the 3i into the parenthesis
so, 6i + 15(i * i) = x + 6i
remember that i * i = -1 since i is the square root of negative one.
so now you have
-15 + 6i = x + 6i
Any number can be expressed in terms of imaginary and real numbers so the real component is any number that doesn't have the i coefficient so we can set the real numbers equal to each other so
-15 = x. voila!

Answer 2

A. –15
------------
Reason: 3i(2+5i) = 6i-15 = x + 6i. Subtracting 6i from both sides gives, x = -15. Remember 3i(5i) = 15i^2 = -15 because i^2 = -1.

Answer 3

Multiply it out:

3i*(2 + 5i) = 6i - 15

since x is the real part of the right side, it must equal the real part of the left, which is -15

Answer 4

i is a mathematical term for the square root of -1

expanding the equation
6i + 15i**2 =6i = x

15i**2 = x (ie 15 times i squared - it's a bit hard on here)

as i = square root -1
i squared = -1

x = 15 times -1 = -15

Answer 5

Here is how the answer is derived:

If i=1

6i+15i=x+6i
21i=x+6i
x=6i-21i
x=-15

Answer 6

...15 i...D.