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Title: Powers
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Series: Complex Analysis
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YouTube-Title: Complex Analysis 14 | Powers
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Bright video: https://youtu.be/qRccImZr_YE
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Dark video: https://youtu.be/DcLHAUwzlb8
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Ad-free video: Watch Vimeo video
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Quiz: Test your knowledge
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Dark-PDF: Download PDF version of the dark video
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Print-PDF: Download printable PDF version
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Thumbnail (bright): Download PNG
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Thumbnail (dark): Download PNG
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Subtitle on GitHub: ca14_sub_eng.srt missing
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Timestamps
00:00 Intro
00:14 Powers with complex numbers
01:06 Power definition in the real numbers
03:45 Using logarithm to write powers
04:50 Power definition in the complex numbers
06:05 What to do with a complex base?
07:00 Principal value of the power function
08:48 Credits
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Subtitle in English (n/a)
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Quiz Content
Q1: What is $i^4$?
A1: $i$
A2: $1$
A3: $-1$
A4: $-i$
Q2: What is $e^{i \pi}$?
A1: $1$
A2: $-1$
A3: $e$
A4: $0$
Q3: Consider the principal value of the power. What is $i^i$?
A1: $0$
A2: $\frac{\pi}{2}$
A3: $\exp \left( -\frac{\pi}{2} \right)$
A4: $\exp \left( i \frac{\pi}{2} \right)$
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Last update: 2024-10
