Write in Standard Form 2/(1+i)-3/(1-i)

Problem

2/(1+i)−3/(1−i)

Solution

1. Find a common denominator by multiplying the two denominators together.

Denominator=(1+i)*(1−i)

2. Expand the denominator using the difference of squares property and the fact that i2=−1

(1+i)*(1−i)=1−i2

1−(−1)=2

3. Rewrite the fractions with the common denominator by multiplying the numerator of each term by the conjugate of its denominator.

(2*(1−i)−3*(1+i))/2

4. Distribute the constants in the numerator.

(2−2*i−3−3*i)/2

5. Combine like terms in the numerator by grouping the real parts and the imaginary parts.

((2−3)+(−2*i−3*i))/2

(−1−5*i)/2

6. Split the fraction to write the complex number in standard form a+b*i

−1/2−5/2*i

Final Answer

2/(1+i)−3/(1−i)=−1/2−5/2*i

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