Find numerical values (to 4 sig fig.) for a and b?

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To find the numerical values of a and b in the equation a + ib = [(3 + i)/(5 + i)]^5, participants emphasize the importance of showing all calculations step-by-step. The discussion highlights the need for clarity in mathematical processes to adhere to forum rules. Several users suggest breaking down the complex fraction and converting it into polar form for easier exponentiation. The final values for a and b should be expressed to four significant figures. Participants encourage thorough explanations to enhance understanding and learning.
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a+ib=[(3+i)/(5+i)]5

Thanks.
 
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qablos said:
a+ib=[(3+i)/(5+i)]5

Thanks.

You need to show your work. Read the Forum Rules.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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