Bepaal modulus en argument

Hoofdmenu Eentje per keer  🖨

Bepaal modulus en argument

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

---

Bepaal modulus en argument

Verbetersleutel

1. \(-4+6i\\ r = \sqrt{(-4)^2+6^2} = \sqrt{52} \\ \alpha = tan^{-1}(\frac{6}{-4}) \Leftrightarrow \alpha =123^\circ 41' 24{,}2"\text{ of } \alpha = 303^\circ 41' 24{,}2"\\-4+6i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 123^\circ 41' 24{,}2"\)
2. \(-9+10i\\ r = \sqrt{(-9)^2+10^2} = \sqrt{181} \\ \alpha = tan^{-1}(\frac{10}{-9}) \Leftrightarrow \alpha =131^\circ 59' 14"\text{ of } \alpha = 311^\circ 59' 14"\\-9+10i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 131^\circ 59' 14"\)
3. \(-1-i\\ r = \sqrt{(-1)^2+(-1)^2} = \sqrt{2} \\ \alpha = tan^{-1}(\frac{-1}{-1}) \Leftrightarrow \alpha =45^\circ \text{ of } \alpha = 225^\circ \\-1-i\text{ ligt in kwadrant }3, \alpha \text{ ligt dus tussen }180^\circ \text{ en }270^\circ\\ \alpha = 225^\circ \)
4. \(-10+3i\\ r = \sqrt{(-10)^2+3^2} = \sqrt{109} \\ \alpha = tan^{-1}(\frac{3}{-10}) \Leftrightarrow \alpha =163^\circ 18' 2{,}7"\text{ of } \alpha = 343^\circ 18' 2{,}7"\\-10+3i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 163^\circ 18' 2{,}7"\)
5. \(-1+6i\\ r = \sqrt{(-1)^2+6^2} = \sqrt{37} \\ \alpha = tan^{-1}(\frac{6}{-1}) \Leftrightarrow \alpha =99^\circ 27' 44{,}4"\text{ of } \alpha = 279^\circ 27' 44{,}4"\\-1+6i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 99^\circ 27' 44{,}4"\)
6. \(10+9i\\ r = \sqrt{10^2+9^2} = \sqrt{181} \\ \alpha = tan^{-1}(\frac{9}{10}) \Leftrightarrow \alpha =41^\circ 59' 14"\text{ of } \alpha = 221^\circ 59' 14"\\10+9i\text{ ligt in kwadrant }1, \alpha \text{ ligt dus tussen }0^\circ \text{ en }90^\circ\\ \alpha = 41^\circ 59' 14"\)
7. \(-6+10i\\ r = \sqrt{(-6)^2+10^2} = \sqrt{136} \\ \alpha = tan^{-1}(\frac{10}{-6}) \Leftrightarrow \alpha =120^\circ 57' 49{,}5"\text{ of } \alpha = 300^\circ 57' 49{,}5"\\-6+10i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 120^\circ 57' 49{,}5"\)
8. \(10-7i\\ r = \sqrt{10^2+(-7)^2} = \sqrt{149} \\ \alpha = tan^{-1}(\frac{-7}{10}) \Leftrightarrow \alpha =145^\circ 0' 28{,}7"\text{ of } \alpha = 325^\circ 0' 28{,}7"\\10-7i\text{ ligt in kwadrant }4, \alpha \text{ ligt dus tussen }270^\circ \text{ en }360^\circ\\ \alpha = 325^\circ 0' 28{,}7"\)
9. \(10+9i\\ r = \sqrt{10^2+9^2} = \sqrt{181} \\ \alpha = tan^{-1}(\frac{9}{10}) \Leftrightarrow \alpha =41^\circ 59' 14"\text{ of } \alpha = 221^\circ 59' 14"\\10+9i\text{ ligt in kwadrant }1, \alpha \text{ ligt dus tussen }0^\circ \text{ en }90^\circ\\ \alpha = 41^\circ 59' 14"\)
10. \(2-9i\\ r = \sqrt{2^2+(-9)^2} = \sqrt{85} \\ \alpha = tan^{-1}(\frac{-9}{2}) \Leftrightarrow \alpha =102^\circ 31' 43{,}7"\text{ of } \alpha = 282^\circ 31' 43{,}7"\\2-9i\text{ ligt in kwadrant }4, \alpha \text{ ligt dus tussen }270^\circ \text{ en }360^\circ\\ \alpha = 282^\circ 31' 43{,}7"\)
11. \(-5-8i\\ r = \sqrt{(-5)^2+(-8)^2} = \sqrt{89} \\ \alpha = tan^{-1}(\frac{-8}{-5}) \Leftrightarrow \alpha =57^\circ 59' 40{,}6"\text{ of } \alpha = 237^\circ 59' 40{,}6"\\-5-8i\text{ ligt in kwadrant }3, \alpha \text{ ligt dus tussen }180^\circ \text{ en }270^\circ\\ \alpha = 237^\circ 59' 40{,}6"\)
12. \(9-5i\\ r = \sqrt{9^2+(-5)^2} = \sqrt{106} \\ \alpha = tan^{-1}(\frac{-5}{9}) \Leftrightarrow \alpha =150^\circ 56' 43{,}4"\text{ of } \alpha = 330^\circ 56' 43{,}4"\\9-5i\text{ ligt in kwadrant }4, \alpha \text{ ligt dus tussen }270^\circ \text{ en }360^\circ\\ \alpha = 330^\circ 56' 43{,}4"\)