Complex Functions - Complex Analysis
Card 1 of 8
What does the sum below equal?
Another way of asking this question is what is the sum of the 
roots of unity.
What does the sum below equal?
Another way of asking this question is what is the sum of the
Tap to reveal answer
As messy as it looks, this is just a geometric series.
we will use the partial sum formula for the geometric series.
the red part is the only part that matters....the 
cancel out leaving....
and...
thus we have...
which gives the answer of zero.
As messy as it looks, this is just a geometric series.
we will use the partial sum formula for the geometric series.
the red part is the only part that matters....the
and...
thus we have...
which gives the answer of zero.
← Didn't Know|Knew It →
Consider the function 
Find an expression for 
(hint: use the definition of derivatve) and where it exists in the complex plane.
Consider the function
Find an expression for
Tap to reveal answer
Applying the definition of derivative, we have that
![](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/1060649/gif.latex "f'(z) = $\lim_{\Delta z \to 0}$ $\frac{f(z+\Delta z) - f(z)}{\Delta z}$ \")
If the limits exists, it can be found by letting 
approach 
in any manner.
In particular, if we it approach through the points 
, we have that
A similar approach with 
implies that 
Since limits are unique, these two approaches imply that
, which implies 
and 
cannot exist when 
Applying the definition of derivative, we have that
If the limits exists, it can be found by letting
In particular, if we it approach through the points
A similar approach with
Since limits are unique, these two approaches imply that
← Didn't Know|Knew It →
What does the sum below equal?
Another way of asking this question is what is the sum of the roots of unity.
What does the sum below equal?
Another way of asking this question is what is the sum of the
Tap to reveal answer
As messy as it looks, this is just a geometric series.
we will use the partial sum formula for the geometric series.
the red part is the only part that matters....the cancel out leaving....
and...
thus we have...
which gives the answer of zero.
As messy as it looks, this is just a geometric series.
we will use the partial sum formula for the geometric series.
the red part is the only part that matters....the
and...
thus we have...
which gives the answer of zero.
← Didn't Know|Knew It →
Consider the function
Find an expression for (hint: use the definition of derivatve) and where it exists in the complex plane.
Consider the function
Find an expression for
Tap to reveal answer
Applying the definition of derivative, we have that
If the limits exists, it can be found by letting approach in any manner.
In particular, if we it approach through the points , we have that
A similar approach with implies that
Since limits are unique, these two approaches imply that
, which implies and cannot exist when
Applying the definition of derivative, we have that
If the limits exists, it can be found by letting
In particular, if we it approach through the points
A similar approach with
Since limits are unique, these two approaches imply that
← Didn't Know|Knew It →
What does the sum below equal?
Another way of asking this question is what is the sum of the roots of unity.
What does the sum below equal?
Another way of asking this question is what is the sum of the
Tap to reveal answer
As messy as it looks, this is just a geometric series.
we will use the partial sum formula for the geometric series.
the red part is the only part that matters....the cancel out leaving....
and...
thus we have...
which gives the answer of zero.
As messy as it looks, this is just a geometric series.
we will use the partial sum formula for the geometric series.
the red part is the only part that matters....the
and...
thus we have...
which gives the answer of zero.
← Didn't Know|Knew It →
Consider the function
Find an expression for (hint: use the definition of derivatve) and where it exists in the complex plane.
Consider the function
Find an expression for
Tap to reveal answer
Applying the definition of derivative, we have that
If the limits exists, it can be found by letting approach in any manner.
In particular, if we it approach through the points , we have that
A similar approach with implies that
Since limits are unique, these two approaches imply that
, which implies and cannot exist when
Applying the definition of derivative, we have that
If the limits exists, it can be found by letting
In particular, if we it approach through the points
A similar approach with
Since limits are unique, these two approaches imply that
← Didn't Know|Knew It →
What does the sum below equal?
Another way of asking this question is what is the sum of the roots of unity.
What does the sum below equal?
Another way of asking this question is what is the sum of the
Tap to reveal answer
As messy as it looks, this is just a geometric series.
we will use the partial sum formula for the geometric series.
the red part is the only part that matters....the cancel out leaving....
and...
thus we have...
which gives the answer of zero.
As messy as it looks, this is just a geometric series.
we will use the partial sum formula for the geometric series.
the red part is the only part that matters....the
and...
thus we have...
which gives the answer of zero.
← Didn't Know|Knew It →
Consider the function
Find an expression for (hint: use the definition of derivatve) and where it exists in the complex plane.
Consider the function
Find an expression for
Tap to reveal answer
Applying the definition of derivative, we have that
If the limits exists, it can be found by letting approach in any manner.
In particular, if we it approach through the points , we have that
A similar approach with implies that
Since limits are unique, these two approaches imply that
, which implies and cannot exist when
Applying the definition of derivative, we have that
If the limits exists, it can be found by letting
In particular, if we it approach through the points
A similar approach with
Since limits are unique, these two approaches imply that
← Didn't Know|Knew It →