From eb85885d6eb06a2cbe5060a1966353f2c2f05e1b Mon Sep 17 00:00:00 2001 From: Michael Wimmer <m.t.wimmer@tudelft.nl> Date: Sun, 30 Aug 2020 21:28:42 +0000 Subject: [PATCH] Fix missing i in expression for sine. Closes #5 --- src/1_complex_numbers.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/1_complex_numbers.md b/src/1_complex_numbers.md index af83ebd..50bbdea 100644 --- a/src/1_complex_numbers.md +++ b/src/1_complex_numbers.md @@ -173,7 +173,7 @@ As a result, $y$ is only defined up to $2\pi$. Furthermore, we can define the sine and cosine in terms of complex exponentials: $$\cos(x) = \frac{e^{{\rm i} x} + e^{-{\rm i} x}}{2}$$ -$$\sin(x) = \frac{e^{{\rm i} x} - e^{-{\rm i} x}}{2}$$ +$$\sin(x) = \frac{e^{{\rm i} x} - e^{-{\rm i} x}}{2i}$$ Most operations on complex numbers are easiest when converting the complex number to its *polar form*, using the exponential. Some operations which are common in real analysis are then easily derived for their complex counterparts: -- GitLab