Write in Standard Form 2/(3-i)

Problem

2/(3−i)

Solution

1. Identify the complex conjugate of the denominator. The conjugate of 3−i is 3+i

2. Multiply both the numerator and the denominator by this conjugate to eliminate the imaginary unit from the denominator.

2/(3−i)⋅(3+i)/(3+i)

3. Distribute the numerator and expand the denominator using the difference of squares property (a−b*i)*(a+b*i)=a2+b2

(2*(3+i))/(3−i2)

4. Simplify the denominator by substituting i2=−1

(6+2*i)/(9−(−1))

(6+2*i)/10

5. Divide each term in the numerator by the denominator to write the expression in standard form a+b*i

6/10+2/10*i

6. Reduce the fractions to their simplest form.

3/5+1/5*i

Final Answer

2/(3−i)=3/5+1/5*i

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