Evaluate (5−7i)4(5−7𝑖)4 and leave your answer in polar form with the angle in degrees and all numbers rounded to the nearest whole number.
Question
Evaluate (5−7i)4(5−7𝑖)4 and leave your answer in polar form with the angle in degrees and all numbers rounded to the nearest whole number.
Solution
First, let's simplify the expression (5-7i)^4.
Step 1: We know that (a-b)^4 = a^4 - 4a^3b + 6a^2b^2 - 4ab^3 + b^4.
Applying this formula, we get: (5-7i)^4 = 5^4 - 45^3(-7i) + 6*5
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