Write in Standard Form 5/(2-i)

Problem

5/(2−i)

Solution

1. Identify the goal, which is to write the complex fraction in standard form a+b*i by eliminating the imaginary unit from the denominator.

2. Determine the conjugate of the denominator 2 - i,w*h*i*c*h*i*s() + i$.

3. Multiply both the numerator and the denominator by this conjugate.

5/(2−i)⋅(2+i)/(2+i)

4. Distribute the numerator.

5*(2+i)=10+5*i

5. Expand the denominator using the difference of squares property (a−b*i)*(a+b*i)=a2+b2

(2−i)*(2+i)=2−i2

6. Substitute i2=−1 into the denominator expression.

4−(−1)=5

7. Simplify the fraction by dividing both terms in the numerator by the denominator.

(10+5*i)/5=10/5+(5*i)/5

8. Reduce the terms to reach the final standard form.

2+i

Final Answer

5/(2−i)=2+i

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