Bepaal modulus en argument

Hoofdmenu Eentje per keer  🖨

Bepaal modulus en argument

1. \(9-4i\)
2. \(2+10i\)
3. \(-5+5i\)
4. \(5-2i\)
5. \(-5+5i\)
6. \(2-10i\)
7. \(7-7i\)
8. \(7\)
9. \(-10-2i\)
10. \(-3-7i\)
11. \(-2-i\)
12. \(1-3i\)

---

Bepaal modulus en argument

Verbetersleutel

1. \(9-4i\\ r = \sqrt{9^2+(-4)^2} = \sqrt{97} \\ \alpha = tan^{-1}(\frac{-4}{9}) \Leftrightarrow \alpha =156^\circ 2' 15"\text{ of } \alpha = 336^\circ 2' 15"\\9-4i\text{ ligt in kwadrant }4, \alpha \text{ ligt dus tussen }270^\circ \text{ en }360^\circ\\ \alpha = 336^\circ 2' 15"\)
2. \(2+10i\\ r = \sqrt{2^2+10^2} = \sqrt{104} \\ \alpha = tan^{-1}(\frac{10}{2}) \Leftrightarrow \alpha =78^\circ 41' 24{,}2"\text{ of } \alpha = 258^\circ 41' 24{,}2"\\2+10i\text{ ligt in kwadrant }1, \alpha \text{ ligt dus tussen }0^\circ \text{ en }90^\circ\\ \alpha = 78^\circ 41' 24{,}2"\)
3. \(-5+5i\\ r = \sqrt{(-5)^2+5^2} = \sqrt{50} \\ \alpha = tan^{-1}(\frac{5}{-5}) \Leftrightarrow \alpha =135^\circ \text{ of } \alpha = 315^\circ \\-5+5i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 135^\circ \)
4. \(5-2i\\ r = \sqrt{5^2+(-2)^2} = \sqrt{29} \\ \alpha = tan^{-1}(\frac{-2}{5}) \Leftrightarrow \alpha =158^\circ 11' 54{,}9"\text{ of } \alpha = 338^\circ 11' 54{,}9"\\5-2i\text{ ligt in kwadrant }4, \alpha \text{ ligt dus tussen }270^\circ \text{ en }360^\circ\\ \alpha = 338^\circ 11' 54{,}9"\)
5. \(-5+5i\\ r = \sqrt{(-5)^2+5^2} = \sqrt{50} \\ \alpha = tan^{-1}(\frac{5}{-5}) \Leftrightarrow \alpha =135^\circ \text{ of } \alpha = 315^\circ \\-5+5i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 135^\circ \)
6. \(2-10i\\ r = \sqrt{2^2+(-10)^2} = \sqrt{104} \\ \alpha = tan^{-1}(\frac{-10}{2}) \Leftrightarrow \alpha =101^\circ 18' 35{,}8"\text{ of } \alpha = 281^\circ 18' 35{,}8"\\2-10i\text{ ligt in kwadrant }4, \alpha \text{ ligt dus tussen }270^\circ \text{ en }360^\circ\\ \alpha = 281^\circ 18' 35{,}8"\)
7. \(7-7i\\ r = \sqrt{7^2+(-7)^2} = \sqrt{98} \\ \alpha = tan^{-1}(\frac{-7}{7}) \Leftrightarrow \alpha =135^\circ \text{ of } \alpha = 315^\circ \\7-7i\text{ ligt in kwadrant }4, \alpha \text{ ligt dus tussen }270^\circ \text{ en }360^\circ\\ \alpha = 315^\circ \)
8. \(7\\ \text{ Dit complex getal ligt op het positief gedeelte van de x-as. We hebben geen berekeningen nodig om r of } \alpha \text{ te berekenen.} \\\text{r = }7\\\alpha = 0 ^\circ \\\)
9. \(-10-2i\\ r = \sqrt{(-10)^2+(-2)^2} = \sqrt{104} \\ \alpha = tan^{-1}(\frac{-2}{-10}) \Leftrightarrow \alpha =11^\circ 18' 35{,}8"\text{ of } \alpha = 191^\circ 18' 35{,}8"\\-10-2i\text{ ligt in kwadrant }3, \alpha \text{ ligt dus tussen }180^\circ \text{ en }270^\circ\\ \alpha = 191^\circ 18' 35{,}8"\)
10. \(-3-7i\\ r = \sqrt{(-3)^2+(-7)^2} = \sqrt{58} \\ \alpha = tan^{-1}(\frac{-7}{-3}) \Leftrightarrow \alpha =66^\circ 48' 5{,}1"\text{ of } \alpha = 246^\circ 48' 5{,}1"\\-3-7i\text{ ligt in kwadrant }3, \alpha \text{ ligt dus tussen }180^\circ \text{ en }270^\circ\\ \alpha = 246^\circ 48' 5{,}1"\)
11. \(-2-i\\ r = \sqrt{(-2)^2+(-1)^2} = \sqrt{5} \\ \alpha = tan^{-1}(\frac{-1}{-2}) \Leftrightarrow \alpha =26^\circ 33' 54{,}2"\text{ of } \alpha = 206^\circ 33' 54{,}2"\\-2-i\text{ ligt in kwadrant }3, \alpha \text{ ligt dus tussen }180^\circ \text{ en }270^\circ\\ \alpha = 206^\circ 33' 54{,}2"\)
12. \(1-3i\\ r = \sqrt{1^2+(-3)^2} = \sqrt{10} \\ \alpha = tan^{-1}(\frac{-3}{1}) \Leftrightarrow \alpha =108^\circ 26' 5{,}8"\text{ of } \alpha = 288^\circ 26' 5{,}8"\\1-3i\text{ ligt in kwadrant }4, \alpha \text{ ligt dus tussen }270^\circ \text{ en }360^\circ\\ \alpha = 288^\circ 26' 5{,}8"\)