Evaluate the fraction 2i/(1+i)

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We have the fraction 2i/(1 + i)

Making the denominator a real number

2i/(1 + i)

=> 2i( 1 - i)/(1 + i)(1 - i)

=> (2i - 2i^2) / 1 - i^2

=> (2i + 2)/ ( 1 + 1)

=> 1 + i

Therefore we get (1 + i)

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giorgiana1976 | Student

We notice that the fraction has at numerator and denominator, a complex number. Since we are not allowed to keep a complex number at denominator, this one has to be multiplied by it's conjugate, which in this case is (1-i).

2 i/(1+i)=2i*(1-i)/(1-i)*(1+i)

(2i - 2i^2)/(1-i^2)

We know that i^2=-1

So, the number will be:

(2i - 2i^2)/(1-i^2)=(2i+2)/(1+1)=2(1+i)/2

We'll simplify and we'll get:

According to evaluation, the value of the given ratio is:

2i/(1+i) = 1+i

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