- #1
soopo
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Homework Statement
Why do you need to use Cauchy-Riemann in the derivate of [itex] x^3 + i(1-y)^3[/itex], while not in the derivate of [itex] \frac { 1 } {z^2 + 1}[/itex] in using the quotient rule?
where z = x + iy.
I derivated the first expression implicitly in the exam which resulted in zero points of the exercise.
The Attempt at a Solution
I would derivate the latter by expanding the denominator such that
[tex] \frac{1} { (x+iy)^2 +1} =...= \frac {x^2 - y^2 +1} {x^4 + y^4 - 6x^2 y^2 +1} - \frac {2xyi} {x^4 + y^4 -6x^2 y^2 +1} [/tex]
and then derivate as real and then as complex.
The expression is rather challenging at the moment.
I am not sure what is the best way to derivate the latter statement correctly.
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