Simplify (5-2i)^2

Problem

(5−2*i)2

Solution

1. Identify the expression as a binomial square of the form (a−b)2 where a=5 and b=2*i

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

3. Substitute the values into the formula:

(5)2−2*(5)*(2*i)+(2*i)2

4. Evaluate each term:

25−20*i+4*i2

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

25−20*i+4*(−1)

6. Simplify the real parts by combining 25 and −4

21−20*i

Final Answer

(5−2*i)2=21−20*i

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