Simplify the complex fraction 8i/(2-2i)?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

To simplify 8i/(2 - 2i) we have to convert the denominator to a real number. This can be done by multiplying it and the numerator by the complex conjugate or 2 + 2i

8i/(2 - 2i)

=> 8i(2 + 2i)/(2 - 2i)(2 + 2i)

=> (16i + 16i^2)/ (4 - 4i^2)

=> (16i - 16)/ (4 + 4)

=> (16i - 16)/8

=> 2i - 2

The simplified form of the given fraction is 2i - 2

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll factorize the denominator by 2:

8i/2(1-i)

We'll simplify by 2:

4i/(1-i)

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).

4i/(1-i)=4i*(1+i)/(1-i)*(1+i)

(4i + 4i^2)/(1-i^2)

We know that i^2=-1

Therefore, the number will become:

(4i + 4i^2)/(1-i^2)=(4i-4)/(1+1)=4(-1+i)/2

We'll simplify and we'll get:

4(-1+i)/2 = -2 + 2i

The simplified value of the given fraction is: 8i/(2-2i) = -2 + 2i

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