We know the range of sin(x) is between -1 and 1, inclusively, but that’s just with real numbers x. What if our input for the sine function is a complex number? In fact, we can derive the complex definition of sine from the Euler’s formula and we can write sin(z) in terms of complex exponential (e^(iz)-e^(-iz))/(2i) and we will be able to solve sin(z)=2.
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This is my equation of the year in 2017.
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#equationoftheyear
-ln(2 -sqrt(3)),
Euler’s formula:
*Sorry I forgot the square root. |z| =sqrt(a^2 b^2)
**Also, I should have written the horizontal axis as “Re“ and the vertical axis as “Im“
***The last time I did complex analysis was back in 2012
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