Bepaal modulus en argument

Hoofdmenu Eentje per keer  🖨

Bepaal modulus en argument

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

---

Bepaal modulus en argument

Verbetersleutel

1. \(4+8i\\ r = \sqrt{4^2+8^2} = \sqrt{80} \\ \alpha = tan^{-1}(\frac{8}{4}) \Leftrightarrow \alpha =63^\circ 26' 5{,}8"\text{ of } \alpha = 243^\circ 26' 5{,}8"\\4+8i\text{ ligt in kwadrant }1, \alpha \text{ ligt dus tussen }0^\circ \text{ en }90^\circ\\ \alpha = 63^\circ 26' 5{,}8"\)
2. \(-10+2i\\ r = \sqrt{(-10)^2+2^2} = \sqrt{104} \\ \alpha = tan^{-1}(\frac{2}{-10}) \Leftrightarrow \alpha =168^\circ 41' 24{,}2"\text{ of } \alpha = 348^\circ 41' 24{,}2"\\-10+2i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 168^\circ 41' 24{,}2"\)
3. \(10-5i\\ r = \sqrt{10^2+(-5)^2} = \sqrt{125} \\ \alpha = tan^{-1}(\frac{-5}{10}) \Leftrightarrow \alpha =153^\circ 26' 5{,}8"\text{ of } \alpha = 333^\circ 26' 5{,}8"\\10-5i\text{ ligt in kwadrant }4, \alpha \text{ ligt dus tussen }270^\circ \text{ en }360^\circ\\ \alpha = 333^\circ 26' 5{,}8"\)
4. \(-8-i\\ r = \sqrt{(-8)^2+(-1)^2} = \sqrt{65} \\ \alpha = tan^{-1}(\frac{-1}{-8}) \Leftrightarrow \alpha =7^\circ 7' 30{,}1"\text{ of } \alpha = 187^\circ 7' 30{,}1"\\-8-i\text{ ligt in kwadrant }3, \alpha \text{ ligt dus tussen }180^\circ \text{ en }270^\circ\\ \alpha = 187^\circ 7' 30{,}1"\)
5. \(2-2i\\ r = \sqrt{2^2+(-2)^2} = \sqrt{8} \\ \alpha = tan^{-1}(\frac{-2}{2}) \Leftrightarrow \alpha =135^\circ \text{ of } \alpha = 315^\circ \\2-2i\text{ ligt in kwadrant }4, \alpha \text{ ligt dus tussen }270^\circ \text{ en }360^\circ\\ \alpha = 315^\circ \)
6. \(7+8i\\ r = \sqrt{7^2+8^2} = \sqrt{113} \\ \alpha = tan^{-1}(\frac{8}{7}) \Leftrightarrow \alpha =48^\circ 48' 50{,}7"\text{ of } \alpha = 228^\circ 48' 50{,}7"\\7+8i\text{ ligt in kwadrant }1, \alpha \text{ ligt dus tussen }0^\circ \text{ en }90^\circ\\ \alpha = 48^\circ 48' 50{,}7"\)
7. \(-2+4i\\ r = \sqrt{(-2)^2+4^2} = \sqrt{20} \\ \alpha = tan^{-1}(\frac{4}{-2}) \Leftrightarrow \alpha =116^\circ 33' 54{,}2"\text{ of } \alpha = 296^\circ 33' 54{,}2"\\-2+4i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 116^\circ 33' 54{,}2"\)
8. \(-2-5i\\ r = \sqrt{(-2)^2+(-5)^2} = \sqrt{29} \\ \alpha = tan^{-1}(\frac{-5}{-2}) \Leftrightarrow \alpha =68^\circ 11' 54{,}9"\text{ of } \alpha = 248^\circ 11' 54{,}9"\\-2-5i\text{ ligt in kwadrant }3, \alpha \text{ ligt dus tussen }180^\circ \text{ en }270^\circ\\ \alpha = 248^\circ 11' 54{,}9"\)
9. \(-1-6i\\ r = \sqrt{(-1)^2+(-6)^2} = \sqrt{37} \\ \alpha = tan^{-1}(\frac{-6}{-1}) \Leftrightarrow \alpha =80^\circ 32' 15{,}6"\text{ of } \alpha = 260^\circ 32' 15{,}6"\\-1-6i\text{ ligt in kwadrant }3, \alpha \text{ ligt dus tussen }180^\circ \text{ en }270^\circ\\ \alpha = 260^\circ 32' 15{,}6"\)
10. \(-10+6i\\ r = \sqrt{(-10)^2+6^2} = \sqrt{136} \\ \alpha = tan^{-1}(\frac{6}{-10}) \Leftrightarrow \alpha =149^\circ 2' 10{,}5"\text{ of } \alpha = 329^\circ 2' 10{,}5"\\-10+6i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 149^\circ 2' 10{,}5"\)
11. \(3-3i\\ r = \sqrt{3^2+(-3)^2} = \sqrt{18} \\ \alpha = tan^{-1}(\frac{-3}{3}) \Leftrightarrow \alpha =135^\circ \text{ of } \alpha = 315^\circ \\3-3i\text{ ligt in kwadrant }4, \alpha \text{ ligt dus tussen }270^\circ \text{ en }360^\circ\\ \alpha = 315^\circ \)
12. \(-4-4i\\ r = \sqrt{(-4)^2+(-4)^2} = \sqrt{32} \\ \alpha = tan^{-1}(\frac{-4}{-4}) \Leftrightarrow \alpha =45^\circ \text{ of } \alpha = 225^\circ \\-4-4i\text{ ligt in kwadrant }3, \alpha \text{ ligt dus tussen }180^\circ \text{ en }270^\circ\\ \alpha = 225^\circ \)