Simplify (3-4i)^2

Problem

(3−4*i)2

Solution

1. Identify the expression as a binomial square of the form (a−b)2 where a=3 and b=4*i

2. Apply the formula for the square of a binomial: (a−b)2=a2−2*a*b+b2

3. Substitute the values into the formula:

(3)2−2*(3)*(4*i)+(4*i)2

4. Evaluate the individual terms:

9−24*i+16*i2

5. Apply the property of the imaginary unit where i2=−1

9−24*i+16*(−1)

6. Simplify the expression by combining the real numbers:

9−24*i−16

9−16−24*i

−7−24*i

Final Answer

(3−4*i)2=−7−24*i

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