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=a2−2*a*b+b2

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

4. Calculate the squares and the product: 16−24*i+9*i2

5. Recall the definition of the imaginary unit i2=−1

6. Substitute −1 for i2 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

Want more problems? Check here!