Answer:
a = 1
b = 2
Explanation:
i is the imaginary number.
The sqroot(-1) = i
But useful for this problem is that i^2=-1
Also, for this problem we'll keep the right side of the equation just the way it is, change the left side to be in the same order (a plain number + an i term) Then we'll pick out the a and b that make it a true statement.
2a + (b + i)i = 1 + 2i
Distribute the i on the left (i acts just like a variable most of the time, even tho it isn't)
2a + bi + i^2 = 1 + 2i
Remember i^2 is -1.
2a + bi + -1 = 1 + 2i
2a + -1 + bi = 1 + 2i
(2a+-1) is the plain number.
bi is the i term.
2a+-1 = 1 and bi=2i
solve for a.
And b is 2.
2a + -1 +1 = 1+1
2a = 2
a = 1