Explore tens of thousands of sets crafted by our community.
Complex Logarithms and Their Branches
29
Flashcards
0/29
z = 2e^{i\pi/6}
Log(2e^{i\pi/6}) = ln(2) + i(\frac{\pi}{6} + 2k\pi), k \in \mathbb{Z}
z = -1 + i
Log(-1 + i) = ln(\sqrt{2}) + i(\pi + 2k\pi), k \in \mathbb{Z}
z = 2i
Log(2i) = ln(2) + i(\frac{\pi}{2} + 2k\pi), k \in \mathbb{Z}
z = -i
Log(-i) = ln(1) + i(-\frac{\pi}{2} + 2k\pi), k \in \mathbb{Z}
z = 0
Log(0) is undefined.
z = -e^{i\pi/3}
Log(-e^{i\pi/3}) = ln(1) + i(\pi + \frac{\pi}{3} + 2k\pi), k \in \mathbb{Z}
z = -\pi
Log(-\pi) = ln(\pi) + i(\pi + 2k\pi), k \in \mathbb{Z}
z = -1
Log(-1) = ln(1) + i(\pi + 2k\pi), k \in \mathbb{Z}
z = 1 + i\sqrt{3}
Log(1 + i\sqrt{3}) = ln(2) + i(\frac{\pi}{3} + 2k\pi), k \in \mathbb{Z}
z = i
Log(i) = ln(1) + i(\frac{\pi}{2} + 2k\pi), k \in \mathbb{Z}
z = \frac{1}{2} - i\frac{\sqrt{3}}{2}
Log(\frac{1}{2} - i\frac{\sqrt{3}}{2}) = ln(1) + i(-\frac{2\pi}{3} + 2k\pi), k \in \mathbb{Z}
z = -\frac{1}{2} + i\frac{\sqrt{3}}{2}
Log(-\frac{1}{2} + i\frac{\sqrt{3}}{2}) = ln(1) + i(\frac{2\pi}{3} + 2k\pi), k \in \mathbb{Z}
z = -1 - i
Log(-1 - i) = ln(\sqrt{2}) + i(-\frac{3\pi}{4} + 2k\pi), k \in \mathbb{Z}
z = -3i
Log(-3i) = ln(3) + i(-\frac{\pi}{2} + 2k\pi), k \in \mathbb{Z}
z = 3 - 4i
Log(3 - 4i) = ln(5) + i(-0.9273 + 2k\pi), k \in \mathbb{Z}
z = -2 + 2i
Log(-2 + 2i) = ln(\sqrt{8}) + i(\frac{3\pi}{4} + 2k\pi), k \in \mathbb{Z}
z = 0.5 + i0.5
Log(0.5 + i0.5) = ln(\sqrt{0.5}) + i(\frac{\pi}{4} + 2k\pi), k \in \mathbb{Z}
z = 1 - i
Log(1 - i) = ln(\sqrt{2}) + i(-\frac{\pi}{4} + 2k\pi), k \in \mathbb{Z}
z = -2
Log(-2) = ln(2) + i(\pi + 2k\pi), k \in \mathbb{Z}
z = 5i
Log(5i) = ln(5) + i(\frac{\pi}{2} + 2k\pi), k \in \mathbb{Z}
z = -\frac{3}{2} - i\frac{3}{2}
Log(-\frac{3}{2} - i\frac{3}{2}) = ln(\frac{3}{\sqrt{2}}) + i(-\frac{3\pi}{4} + 2k\pi), k \in \mathbb{Z}
z = -\frac{1}{2} - i\frac{\sqrt{3}}{2}
Log(-\frac{1}{2} - i\frac{\sqrt{3}}{2}) = ln(1) + i(-\frac{2\pi}{3} + 2k\pi), k \in \mathbb{Z}
z = 1
Log(1) = ln(1) + i(2k\pi), k \in \mathbb{Z}
z = e^{i\pi/4}
Log(e^{i\pi/4}) = i(\frac{\pi}{4} + 2k\pi), k \in \mathbb{Z}
z = -\sqrt{2} - i\sqrt{2}
Log(-\sqrt{2} - i\sqrt{2}) = ln(2) + i(-\frac{3\pi}{4} + 2k\pi), k \in \mathbb{Z}
z = 8i
Log(8i) = ln(8) + i(\frac{\pi}{2} + 2k\pi), k \in \mathbb{Z}
z = \sqrt{3} - i
Log(\sqrt{3} - i) = ln(2) + i(-\frac{\pi}{6} + 2k\pi), k \in \mathbb{Z}
z = -\sqrt{3} + i
Log(-\sqrt{3} + i) = ln(2) + i(\frac{5\pi}{6} + 2k\pi), k \in \mathbb{Z}
z = 2 + 2i
Log(2 + 2i) = ln(\sqrt{8}) + i(\frac{\pi}{4} + 2k\pi), k \in \mathbb{Z}
© Hypatia.Tech. 2024 All rights reserved.
