Toronto Math Forum
MAT3342020F => MAT334Tests and Quizzes => Quiz 2 => Topic started by: Xinqiao Li on October 03, 2020, 05:47:44 AM

Questions: Find all points of continuity of the given function: $f(z)=(ImzRez)^{1}$
Solutions:
Let $z=x+iy$ where x,y are real numbers.
Then $f(z)=f(x,y)=(Im(x+iy)Re(x+iy))^{1}=(yx)^{1}=\frac{1}{yx}$
The function is not valid when the denominator equals 0, that is, $y=x$.
Therefore, the function is discontinuous only at all points of the line $y=x$.