Simplify (1-2i)^2-(1+2i)^2

Problem

(1−2*i)2−(1+2*i)2

Solution

1. Identify the expression as a difference of squares in the form a2−b2 where a=(1−2*i) and b=(1+2*i)

2. Apply the formula for the difference of squares, which is a2−b2=(a−b)*(a+b)

3. Substitute the values of a and b into the factored form.

((1−2*i)−(1+2*i))*((1−2*i)+(1+2*i))

4. Simplify the terms inside the first set of parentheses by distributing the negative sign.

(1−2*i−1−2*i)

−4*i

5. Simplify the terms inside the second set of parentheses.

(1−2*i+1+2*i)

2

6. Multiply the two resulting simplified terms together.

−4*i⋅2

−8*i

Final Answer

(1−2*i)2−(1+2*i)2=−8*i

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