3.2 Übungen
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Version vom 13:50, 16. Sep. 2008
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Exercise 3.2:1
Given the complex numbers \displaystyle \,z=2+i\,, \displaystyle \,w=2+3i\, and \displaystyle \,u=-1-2i\,. Mark the following numbers on the complex plane:
| a) | \displaystyle z\, och \displaystyle \,w | b) | \displaystyle z+u\, och \displaystyle \,z-u |
| c) | \displaystyle 2z+w | d) | \displaystyle z-\overline{w}+u |
Answer
Laden...
Solution a
Solution b
Solution c
Solution d
Exercise 3.2:2
Draw the following sets in the complex number plane
| a) | \displaystyle 0\le \mbox{Im}\, z \le 3 | b) | \displaystyle 0 \le \mbox{Re} \, z \le \mbox{Im}\, z \le 3 |
| c) | \displaystyle |z|=2 | d) | \displaystyle |z-1-i|=3 |
| e) | \displaystyle \mbox{Re}\, z = i + \bar z | f) | \displaystyle 2<|z-i|\le3 |
Answer
Solution a
Solution b
Solution c
Solution d
Solution e
Solution f
Exercise 3.2:3
The complex numbers \displaystyle \,1+i\,, \displaystyle \,3+2i\, and \displaystyle \,3i\, constitute three corners of a square in the complex number plane. Determine the square's fourth corner.
Answer
Solution
Exercise 3.2:4
Determine the magnitude of
| a) | \displaystyle 3+4i | b) | \displaystyle (2-i) + (5+3i) |
| c) | \displaystyle (3-4i)(3+2i) | d) | \displaystyle \displaystyle\frac{3-4i}{3+2i} |
Answer
Solution a
Solution b
Solution c
Solution d
Exercise 3.2:5
Determine the argument of
| a) | \displaystyle -10 | b) | \displaystyle -2+2i |
| c) | \displaystyle (\sqrt{3} +i)(1-i) | d) | \displaystyle \displaystyle\frac{i}{1+i} |
Answer
Solution a
Solution b
Solution c
Solution d
Exercise 3.2:6
Write the following numbers in polar form
| a) | \displaystyle 3 | b) | \displaystyle -11i |
| c) | \displaystyle -4-4i | d) | \displaystyle \sqrt{10} + \sqrt{30}\,i |
| e) | \displaystyle \displaystyle\frac{1+i\sqrt{3}}{1+i} | f) | \displaystyle \displaystyle\frac{(2+2i)(1+i\sqrt{3}\,)}{3i(\sqrt{12} -2i)} |
Answer
Solution a
Solution b
Solution c
Solution d
Solution e
Solution f
