For i = the square root of -1, if 3i (2 + 5i) = x + 6i, then x = ?
A. –15
B. 5
C. 5i
D. 15i
E. 27i
we will be happy to critique your thinking.
Simplify the left hand side (LHS) from
3i(2+5i)
= 6i + 15i2
= 6i - 15
Equate to the RHS and solve for x.
To solve this equation, let's simplify the expression on the left side of the equation:
3i (2 + 5i) = 3i * 2 + 3i * 5i
To multiply complex numbers, we use the distributive property. In this case, we multiply 3i by both terms inside the parentheses:
= 6i + 15i^2
Since i is defined as the square root of -1, we can simplify i^2 as -1:
= 6i + 15(-1)
Now, let's distribute the -15:
= 6i - 15
Finally, we can rewrite the equation with the simplified expression:
6i - 15 = x + 6i
To isolate x, let's move the terms with x to one side and the other terms to the other side of the equation:
x = (6i - 6i) + 15
The terms 6i and -6i cancel each other out:
x = 15
Therefore, the value of x is 15.