Complex analysis

Algebra Level 3

Given that ( a + b i ) 5 = 3 + 7 i (a+bi)^5 = 3 + 7i and ( b + a i ) 5 = p + q i (b + ai)^5 = p + qi for real numbers p p and q q . Find the value of p − q p - q .


The answer is 4.

Surya Prakash Bugatha by Surya Prakash Bugatha , 22, India

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1 solution

Tanishq Varshney
Jun 27, 2015

given

( a + i b ) 5 = 3 + 7 i (a+ib)^{5}=3+7i

i ( a i + b ) 5 = 3 + 7 i \large{i(\frac{a}{i}+b)^{5}=3+7i}

( b − i a ) 5 = 7 − 3 i (b-ia)^5=7-3i

Taking conjugate on both side

( b + i a ) 5 = 7 + 3 i (b+ia)^5=7+3i

p = 7 p=7 and q = 3 q=3

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