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which of the following are functions are continuous on $f:\mathbb{C}\rightarrow \mathbb{C}$

1.$f(z) = \left\{ \begin{array}{rcl}0 & \mbox{if} & z=0\;or\;|z| \;is \;irrational \\ \frac{1}{q} & \mbox{if} & |z|=\frac{p}{q}\in \mathbb{Q}\backslash\{0\}(written\;in\;the\;lowest\;terms) \end{array}\right.$

2.$f(z) = \left\{ \begin{array}{rcl}0 & \mbox{if} & z=0\;\\ \sin \phi & \mbox{if} & z=re^{i\phi}\neq0 \end{array}\right.$

for first i think f is continuous at |z| is irrational but i am not sure for second function i dont have idea

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    Think about what happens along different lines through the origin. – 2017-02-10
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    @chriseur : you mean like the line y=mx,y=mx^2,,,, – 2017-02-10
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    Just $y=mx$ for different values of $m$ will do. – 2017-02-10
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    @chriseur..i did't get anyting – 2017-02-10

0 Answers 0