Simplify (8-3i)^2

Problem

(8−3*i)2

Solution

1. Identify the expression as a binomial square of the form (a−b)2 where a=8 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:

(8)2−2*(8)*(3*i)+(3*i)2

4. Calculate the squares and the product:

64−48*i+9*i2

5. Recall the definition of the imaginary unit i2=−1 and substitute it into the expression:

64−48*i+9*(−1)

6. Simplify the real terms by combining 64 and −9

55−48*i

Final Answer

(8−3*i)2=55−48*i

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