Simplify (x+i)^2-(x-i)^2

Problem

(x+i)2−(x−i)2

Solution

1. Expand the first squared binomial (x+i)2 using the identity (a+b)2=a2+2*a*b+b2

(x+i)2=x2+2*x*i+i2

2. Expand the second squared binomial (x−i)2 using the identity (a−b)2=a2−2*a*b+b2

(x−i)2=x2−2*x*i+i2

3. Substitute the expanded forms back into the original expression.

(x2+2*x*i+i2)−(x2−2*x*i+i2)

4. Distribute the negative sign through the second set of parentheses.

x2+2*x*i+i2−x2+2*x*i−i2

5. Combine like terms to simplify the expression.

x2−x2+2*x*i+2*x*i+i2−i2

4*x*i

Final Answer

(x+i)2−(x−i)2=4*x*i

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