Write in Standard Form (4-i)/(2-i)

Problem

(4−i)/(2−i)

Solution

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

2. Multiply the numerator and the denominator by the conjugate of the denominator, which is 2+i

(4−i)/(2−i)⋅(2+i)/(2+i)

3. Expand the numerator using the FOIL method (First, Outer, Inner, Last).

(4−i)*(2+i)=8+4*i−2*i−i2

4. Expand the denominator using the difference of squares pattern.

(2−i)*(2+i)=2−i2

5. Substitute −1 for i2 in both the numerator and the denominator.

(8+2*i−(−1))/(4−(−1))

6. Simplify the real parts and the denominator.

(9+2*i)/5

7. Distribute the denominator to write the expression in the standard form a+b*i

9/5+2/5*i

Final Answer

(4−i)/(2−i)=9/5+2/5*i

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