Bepaal modulus en argument

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Bepaal modulus en argument

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

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Bepaal modulus en argument

Verbetersleutel

1. \(-7-2i\\ r = \sqrt{(-7)^2+(-2)^2} = \sqrt{53} \\ \alpha = tan^{-1}(\frac{-2}{-7}) \Leftrightarrow \alpha =15^\circ 56' 43{,}4"\text{ of } \alpha = 195^\circ 56' 43{,}4"\\-7-2i\text{ ligt in kwadrant }3, \alpha \text{ ligt dus tussen }180^\circ \text{ en }270^\circ\\ \alpha = 195^\circ 56' 43{,}4"\)
2. \(5+2i\\ r = \sqrt{5^2+2^2} = \sqrt{29} \\ \alpha = tan^{-1}(\frac{2}{5}) \Leftrightarrow \alpha =21^\circ 48' 5{,}1"\text{ of } \alpha = 201^\circ 48' 5{,}1"\\5+2i\text{ ligt in kwadrant }1, \alpha \text{ ligt dus tussen }0^\circ \text{ en }90^\circ\\ \alpha = 21^\circ 48' 5{,}1"\)
3. \(-7+6i\\ r = \sqrt{(-7)^2+6^2} = \sqrt{85} \\ \alpha = tan^{-1}(\frac{6}{-7}) \Leftrightarrow \alpha =139^\circ 23' 55{,}3"\text{ of } \alpha = 319^\circ 23' 55{,}3"\\-7+6i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 139^\circ 23' 55{,}3"\)
4. \(1-4i\\ r = \sqrt{1^2+(-4)^2} = \sqrt{17} \\ \alpha = tan^{-1}(\frac{-4}{1}) \Leftrightarrow \alpha =104^\circ 2' 10{,}5"\text{ of } \alpha = 284^\circ 2' 10{,}5"\\1-4i\text{ ligt in kwadrant }4, \alpha \text{ ligt dus tussen }270^\circ \text{ en }360^\circ\\ \alpha = 284^\circ 2' 10{,}5"\)
5. \(-6+6i\\ r = \sqrt{(-6)^2+6^2} = \sqrt{72} \\ \alpha = tan^{-1}(\frac{6}{-6}) \Leftrightarrow \alpha =135^\circ \text{ of } \alpha = 315^\circ \\-6+6i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 135^\circ \)
6. \(-8+7i\\ r = \sqrt{(-8)^2+7^2} = \sqrt{113} \\ \alpha = tan^{-1}(\frac{7}{-8}) \Leftrightarrow \alpha =138^\circ 48' 50{,}7"\text{ of } \alpha = 318^\circ 48' 50{,}7"\\-8+7i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 138^\circ 48' 50{,}7"\)
7. \(-3-2i\\ r = \sqrt{(-3)^2+(-2)^2} = \sqrt{13} \\ \alpha = tan^{-1}(\frac{-2}{-3}) \Leftrightarrow \alpha =33^\circ 41' 24{,}2"\text{ of } \alpha = 213^\circ 41' 24{,}2"\\-3-2i\text{ ligt in kwadrant }3, \alpha \text{ ligt dus tussen }180^\circ \text{ en }270^\circ\\ \alpha = 213^\circ 41' 24{,}2"\)
8. \(5-3i\\ r = \sqrt{5^2+(-3)^2} = \sqrt{34} \\ \alpha = tan^{-1}(\frac{-3}{5}) \Leftrightarrow \alpha =149^\circ 2' 10{,}5"\text{ of } \alpha = 329^\circ 2' 10{,}5"\\5-3i\text{ ligt in kwadrant }4, \alpha \text{ ligt dus tussen }270^\circ \text{ en }360^\circ\\ \alpha = 329^\circ 2' 10{,}5"\)
9. \(-6-3i\\ r = \sqrt{(-6)^2+(-3)^2} = \sqrt{45} \\ \alpha = tan^{-1}(\frac{-3}{-6}) \Leftrightarrow \alpha =26^\circ 33' 54{,}2"\text{ of } \alpha = 206^\circ 33' 54{,}2"\\-6-3i\text{ ligt in kwadrant }3, \alpha \text{ ligt dus tussen }180^\circ \text{ en }270^\circ\\ \alpha = 206^\circ 33' 54{,}2"\)
10. \(3-5i\\ r = \sqrt{3^2+(-5)^2} = \sqrt{34} \\ \alpha = tan^{-1}(\frac{-5}{3}) \Leftrightarrow \alpha =120^\circ 57' 49{,}5"\text{ of } \alpha = 300^\circ 57' 49{,}5"\\3-5i\text{ ligt in kwadrant }4, \alpha \text{ ligt dus tussen }270^\circ \text{ en }360^\circ\\ \alpha = 300^\circ 57' 49{,}5"\)
11. \(2-9i\\ r = \sqrt{2^2+(-9)^2} = \sqrt{85} \\ \alpha = tan^{-1}(\frac{-9}{2}) \Leftrightarrow \alpha =102^\circ 31' 43{,}7"\text{ of } \alpha = 282^\circ 31' 43{,}7"\\2-9i\text{ ligt in kwadrant }4, \alpha \text{ ligt dus tussen }270^\circ \text{ en }360^\circ\\ \alpha = 282^\circ 31' 43{,}7"\)
12. \(6+10i\\ r = \sqrt{6^2+10^2} = \sqrt{136} \\ \alpha = tan^{-1}(\frac{10}{6}) \Leftrightarrow \alpha =59^\circ 2' 10{,}5"\text{ of } \alpha = 239^\circ 2' 10{,}5"\\6+10i\text{ ligt in kwadrant }1, \alpha \text{ ligt dus tussen }0^\circ \text{ en }90^\circ\\ \alpha = 59^\circ 2' 10{,}5"\)