How would I solve 2i/(1+i) ?

I know the answer is 1+i but I don't know how to get there.

I know the answer is 1+i but I don't know how to get there.

2i

------

1 + i

2i(1 - i)

----------------- {multiplied top and bottom by conjugate of denominator}

(1 + i)(1 - i)

2i - 2i²

----------------- {used distributive property on top and foil method on bottom}

1 - i²

2i - 2(-1)

------------------ {in imaginary numbers, i² is -1}

1 - (-1)

2i + 2

--------- {simplified on top and bottom}

1 + 1

2(i + 1)

------------ {factored 2 out of top}

2

= i + 1 {cancelled the 2's}

=

------

1 + i

2i(1 - i)

----------------- {multiplied top and bottom by conjugate of denominator}

(1 + i)(1 - i)

2i - 2i²

----------------- {used distributive property on top and foil method on bottom}

1 - i²

2i - 2(-1)

------------------ {in imaginary numbers, i² is -1}

1 - (-1)

2i + 2

--------- {simplified on top and bottom}

1 + 1

2(i + 1)

------------ {factored 2 out of top}

2

= i + 1 {cancelled the 2's}

=

**1 + i**{flipped around}*© Algebra House*