# What are a and b from expression a + b + 2i = i*a - i*b + 6 ?

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a+ b + 2i = i*a - i*b + 6

First we will combine like terms on each side:

==> (a+b) + 2*i = 6 + (a-b) *i

Now compare both sides:

==> a+ b = 6 ..............(1)

==> a-b = 2 .................(2)

Using the elimination method add (1) and (2):

==> 2a = 8

**==> a= 4**

Now substitute in (2) to find b:

a-b = 2 ==> 4-b = 2

==> b= 4-2 = 2

**==> b= 2**

To find a and b in a+b+2i = i*a-i*b+6

We know i = sqrt(-1).

a+b +2i = i*a- i*b +6.

We write both sides in x+yi form where x is real part and y is imaginary part.

(a+b) +2i = 6 +(a-b)i.........(1)

We equate real parts on both side of (1):

a+b = 6...........(2)

We equate imaginary parts on both sides of (1):

2 = a-b. Or

a-b = 2...............(3)

Adding eq(2) and (3) we get:

2a = 8

a = 8/2 = 4

Eq(2) - eq(3) gives:

2b = 6-2 = 4.

b = 4/2 = 2

Therefore a = 4 and b = 2.

To compute a and b, we'll combine, both sides, the real parts and the imaginary parts.

To the left side, the real part is (a+b) and the imaginary part is 2.

(a+b) + 2i = 6 + i*(a-b)

We'll put the real part from the left side equal to the real part from the right side:

a+b = 6 (1)

We'll put the imaginary part from the left side equal to the imaginary part from the right side:

a - b = 2 (2)

We'll add (1)+(2):

a+b+a-b = 6+2

We'll eliminate like terms:

2a = 8

**a = 4**

We'll substitute a=4 into (1):

a+b = 6

4+b = 6

b = 6-4

**b = 2**