Euler's Identity
Knowing the limit definition , explore what happens graphically when k=iπ for some finite values n.
Consider how when we multiply two complex numbers and , the product is .
Or by extension, .
When k is set to iπ and N is set to a "large" value, can you make sense of the resulting geometry? Does it help explain the value of ?
Drag the point representing k to other locations on the complex plane to explore other values.