3.1 Exercises
From Förberedande kurs i matematik 2
(Difference between revisions)
(Translated links into English) |
m (Robot: Automated text replacement (-{{Vald flik +{{Selected tab)) |
||
| (6 intermediate revisions not shown.) | |||
| Line 2: | Line 2: | ||
{| border="0" cellspacing="0" cellpadding="0" height="30" width="100%" | {| border="0" cellspacing="0" cellpadding="0" height="30" width="100%" | ||
| style="border-bottom:1px solid #000" width="5px" | | | style="border-bottom:1px solid #000" width="5px" | | ||
| - | {{ | + | {{Not selected tab|[[3.1 Complex number calculations|Theory]]}} |
| - | {{ | + | {{Selected tab|[[3.1 Exercises|Exercises]]}} |
| style="border-bottom:1px solid #000" width="100%"| | | style="border-bottom:1px solid #000" width="100%"| | ||
|} | |} | ||
| Line 26: | Line 26: | ||
|width="50%"| <math>i^{\,20} + i^{\,11}</math> | |width="50%"| <math>i^{\,20} + i^{\,11}</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Answer| | + | </div>{{#NAVCONTENT:Answer|Answer 3.1:1|Solution a|Solution 3.1:1a|Solution b|Solution 3.1:1b|Solution c|Solution 3.1:1c|Solution d|Solution 3.1:1d|Solution e|Solution 3.1:1e|Solution f|Solution 3.1:1f}} |
===Exercise 3.1:2=== | ===Exercise 3.1:2=== | ||
| Line 42: | Line 42: | ||
|width="50%"| <math>\displaystyle\frac{5-\displaystyle\frac{1}{1+i}}{3i + \displaystyle\frac{i}{2-3i}}</math> | |width="50%"| <math>\displaystyle\frac{5-\displaystyle\frac{1}{1+i}}{3i + \displaystyle\frac{i}{2-3i}}</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Answer| | + | </div>{{#NAVCONTENT:Answer|Answer 3.1:2|Solution a|Solution 3.1:2a|Solution b|Solution 3.1:2b|Solution c|Solution 3.1:2c|Solution d|Solution 3.1:2d}} |
===Exercise 3.1:3=== | ===Exercise 3.1:3=== | ||
| Line 49: | Line 49: | ||
| - | </div>{{#NAVCONTENT:Answer| | + | </div>{{#NAVCONTENT:Answer|Answer 3.1:3|Solution|Solution 3.1:3}} |
===Exercise 3.1:4=== | ===Exercise 3.1:4=== | ||
| Line 70: | Line 70: | ||
|width="50%"| <math>(1+i)\overline{z}+iz = 3+5i</math> | |width="50%"| <math>(1+i)\overline{z}+iz = 3+5i</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Answer| | + | </div>{{#NAVCONTENT:Answer|Answer 3.1:4|Solution a|Solution 3.1:4a|Solution b|Solution 3.1:4b|Solution c|Solution 3.1:4c|Solution d|Solution 3.1:4d|Solution e|Solution 3.1:4e|Solution f|Solution 3.1:4f}} |
Current revision
| Theory | Exercises |
Exercise 3.1:1
Write in the form \displaystyle \,a+bi\,, where \displaystyle \,a\, and \displaystyle \,b\, are real numbers
| a) | \displaystyle (5-2i)+(3+5i) | b) | \displaystyle 3i -(2-i) |
| c) | \displaystyle i(2+3i) | d) | \displaystyle (3-2i)(7+5i) |
| e) | \displaystyle (1+i)(2-i)^2 | f) | \displaystyle i^{\,20} + i^{\,11} |
Answer
Loading...
Solution a
Solution b
Solution c
Solution d
Solution e
Solution f
Exercise 3.1:2
Write in the form \displaystyle \,a+bi\,, where \displaystyle \,a\, and \displaystyle \,b\, are real numbers,
| a) | \displaystyle \displaystyle\frac{3-2i}{1+i} | b) | \displaystyle \displaystyle\frac{3i}{4-6i} - \displaystyle\frac{1+i}{3+2i} |
| c) | \displaystyle \displaystyle\frac{(2-i\sqrt{3}\,)^2}{1+i\sqrt{3}} | d) | \displaystyle \displaystyle\frac{5-\displaystyle\frac{1}{1+i}}{3i + \displaystyle\frac{i}{2-3i}} |
Answer
Solution a
Solution b
Solution c
Solution d
Exercise 3.1:3
Determine the real number \displaystyle \,a\, such that the expression \displaystyle \ \displaystyle\frac{3+i}{2+ai}\ becomes purely imaginary (i.e. the real part equals zero).
Answer
Solution
Exercise 3.1:4
Solve the equations
| a) | \displaystyle z+3i=2z-2 | b) | \displaystyle (2-i) z= 3+2i |
| c) | \displaystyle iz+2= 2z-3 | d) | \displaystyle (2+i) \overline{z} = 1+i |
| e) | \displaystyle \displaystyle\frac{iz+1}{z+i} = 3+i | f) | \displaystyle (1+i)\overline{z}+iz = 3+5i |
Answer
Solution a
Solution b
Solution c
Solution d
Solution e
Solution f
