(New page: Category:complex numbers Category:ECE438 Category:ECE438Fall2011Boutin Category:problem solving = What is the norm of a complex exponential?= After [[Lecture7ECE438F11|clas...) |
|||
| Line 14: | Line 14: | ||
---- | ---- | ||
===Answer 1=== | ===Answer 1=== | ||
| − | + | ||
| + | By Euler's formular | ||
| + | |||
| + | <math> e^{j \omega} = cos(j \omega) + i*sin(j \omega) </math> | ||
| + | |||
| + | hence, | ||
| + | |||
| + | <math>\left| e^{j \omega} \right| = \left|cos(j \omega) + i*sin(j \omega) \right| = \sqrt{cos^2(j \omega) + sin^2(j \omega)} = 1 </math> | ||
| + | |||
===Answer 2=== | ===Answer 2=== | ||
Write it here. | Write it here. | ||
Revision as of 09:09, 10 September 2011
Contents
What is the norm of a complex exponential?
After class today, a student asked me the following question:
$ \left| e^{j \omega} \right| = ? $
Please help answer this question.
You will receive feedback from your instructor and TA directly on this page. Other students are welcome to comment/discuss/point out mistakes/ask questions too!
Answer 1
By Euler's formular
$ e^{j \omega} = cos(j \omega) + i*sin(j \omega) $
hence,
$ \left| e^{j \omega} \right| = \left|cos(j \omega) + i*sin(j \omega) \right| = \sqrt{cos^2(j \omega) + sin^2(j \omega)} = 1 $
Answer 2
Write it here.
Answer 3
Write it here
