Find a and b
2a +( b+i)i= 1+2i

a = 1

b = 2

Step-by-step 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

5

step-by-step explanation:

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8