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rmcclurk
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Homework Statement
Find limit as z->infinity of exp(z) where z is complex
Homework Equations
See above
The Attempt at a Solution
The solution should be that the limit does not exist, but I don't know why. Any explanations?
rmcclurk said:Is it because e^iy = r(cos(y)+i*sin(y)) and that equation simply oscillates and never goes to infinity no matter how large y gets?
The limit of exp(z) as z approaches infinity is equal to infinity.
The limit of exp(z) as z approaches zero is equal to 1.
The limit of exp(z) as z approaches a complex number is equal to the value of exp(z) at that complex number.
The exponential function, denoted as e^z, is equivalent to exp(z), where e is the base of the natural logarithm. Both functions have the same limit as z approaches any real or complex number.
The limit of exp(z) is often used in mathematical models involving growth or decay, such as in population growth or radioactive decay. It can also be used in signal processing and control systems to model exponential behavior.