Perform the indicated operation & simplify. Express the answer in terms of i (as a complex number).(2−7i)2(2-7𝑖)2 =
Question
Perform the indicated operation & simplify. Express the answer in terms of i (as a complex number).(2−7i)2(2-7𝑖)2 =
Solution
To simplify the expression (2-7i)^2, follow these steps:
Step 1: Write down the expression (2-7i)^2
Step 2: Expand the expression using the formula (a-b)^2 = a^2 - 2ab + b^2 = (2)^2 - 2*(2)(7i) + (7i)^2
Step 3: Simplify the expression = 4 - 28i + 49i^2
Step 4: Remember that i^2 = -1 = 4 - 28i - 49
Step 5: Combine like terms = -45 - 28i
So, (2-7i)^2 = -45 - 28i.
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