Math for fun, sin(z)=2
blackpenredpen
1,979,630 views
Access my "100 Everything" ultimate math marathon collection on Patreon: Patreon: 2395510
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.
-ln(2+-sqrt(3)), small problem that i owe you from sin(?)=2
Euler's formula: Euler's Formula (but it's a speedrun)
*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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Math for fun, sin(z)=2
blackpenredpen
1,979,630 views
Access my "100 Everything" ultimate math marathon collection on Patreon: Patreon: 2395510
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.
-ln(2+-sqrt(3)), small problem that i owe you from sin(?)=2
Euler's formula: Euler's Formula (but it's a speedrun)
*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