2i/1+i
your question probably says 'simplify'
multiply top and bottom by (1-i)\(1-i) and remember that i^2 =-1
so...
2i/(1+i) * (1-i)\(1-i)
= (2i - 2i^2)/(1-i^2)
= 2(i-i^2)/(1+1)
=i+1
To simplify the expression 2i/(1+i), we can multiply the numerator and denominator by the conjugate of the denominator, which is (1-i).
By doing this, we eliminate the imaginary unit i in the denominator and simplify the expression.
So, let's proceed:
2i / (1+i) * (1-i) / (1-i)
Now, let's simplify each part step by step:
Numerator:
2i * (1-i) = 2i - 2i^2
We know that i^2 is equal to -1, so substituting that in:
2i - 2(-1) = 2i + 2
Denominator:
(1+i) * (1-i) = 1 - i + i - i^2 = 1 - i + i - (-1) = 1 - (-1) = 1 + 1 = 2
Now, let's combine the simplified numerator and denominator:
(2i + 2) / 2
We can simplify this further by dividing both terms in the numerator by 2:
(2i/2) + (2/2) = i + 1
So, the simplified expression is i + 1.