Simplify (4-3i)^2

Problem

(4−3*i)^2

Solution

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

2. Apply the formula for squaring a binomial: (a−b)^2=a^2−2*a*b+b^2

3. Substitute the values into the formula: 4^2−2*(4)*(3*i)+(3*i)^2

4. Calculate the squares and the product: 16−24*i+9*i^2

5. Recall the definition of the imaginary unit i^2=−1

6. Substitute −1 for i^2 $16 - 24i + 9(-1)$.

7. Simplify the expression by combining the real terms $16 - 9: - 24i$.

Final Answer

(4−3*i)^2=7−24*i

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