Complex Integral??? Hmm..

Calculus Level 4

Given that $Z= x+99i ,$ evaluate

$\displaystyle \int_{101}^{202} \lfloor \arg{ \big|\dfrac{Z-5i}{Z-3}\big|} \rfloor dx$

Note: $\lfloor \ \rfloor$ denotes the greatest integer function.

The answer is 0.

2 solutions

Vijay Raghavan
Mar 25, 2014

This is a pretty simple problem.

The first thing to note is that : The argument of a real number is ZERO .

Here

$\big | \dfrac{Z-5i}{Z-3} \big |$ is a real number.

So, the Integral is $\displaystyle \int^{202}_{101} \lfloor 0 \rfloor {\rm d}x$

$\displaystyle = \boxed{\boxed{0}}$

Correction--- $\left|\frac{Z-5i}{Z-3}\right|$ is a $\textbf{positive real number}$ , and the argument of a $\textbf{positive real number}$ is $0$ .

Pratik Shastri - 7 years ago

Manish Singh
Mar 30, 2014

The value of args|(Z-5i)/Z-3)|= tan^-1[(-5x-282)/(x^2-3x+9306)] which is less than 45 degree that is less than one radian thus greatest value is 0. So the final ans is Zero

vijay raghavan there is no where specified that the two bars mean mod of the complex no though i understood it but may be it could be because of manish singh's answer

Anuva Agrawal - 7 years, 1 month ago

Complex Integral??? Hmm..

The answer is 0.

2 solutions

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