Bepaal modulus en argument

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Bepaal modulus en argument

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

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Bepaal modulus en argument

Verbetersleutel

1. \(3+7i\\ r = \sqrt{3^2+7^2} = \sqrt{58} \\ \alpha = tan^{-1}(\frac{7}{3}) \Leftrightarrow \alpha =66^\circ 48' 5{,}1"\text{ of } \alpha = 246^\circ 48' 5{,}1"\\3+7i\text{ ligt in kwadrant }1, \alpha \text{ ligt dus tussen }0^\circ \text{ en }90^\circ\\ \alpha = 66^\circ 48' 5{,}1"\)
2. \(8-3i\\ r = \sqrt{8^2+(-3)^2} = \sqrt{73} \\ \alpha = tan^{-1}(\frac{-3}{8}) \Leftrightarrow \alpha =159^\circ 26' 38{,}2"\text{ of } \alpha = 339^\circ 26' 38{,}2"\\8-3i\text{ ligt in kwadrant }4, \alpha \text{ ligt dus tussen }270^\circ \text{ en }360^\circ\\ \alpha = 339^\circ 26' 38{,}2"\)
3. \(-4-2i\\ r = \sqrt{(-4)^2+(-2)^2} = \sqrt{20} \\ \alpha = tan^{-1}(\frac{-2}{-4}) \Leftrightarrow \alpha =26^\circ 33' 54{,}2"\text{ of } \alpha = 206^\circ 33' 54{,}2"\\-4-2i\text{ ligt in kwadrant }3, \alpha \text{ ligt dus tussen }180^\circ \text{ en }270^\circ\\ \alpha = 206^\circ 33' 54{,}2"\)
4. \(-8-2i\\ r = \sqrt{(-8)^2+(-2)^2} = \sqrt{68} \\ \alpha = tan^{-1}(\frac{-2}{-8}) \Leftrightarrow \alpha =14^\circ 2' 10{,}5"\text{ of } \alpha = 194^\circ 2' 10{,}5"\\-8-2i\text{ ligt in kwadrant }3, \alpha \text{ ligt dus tussen }180^\circ \text{ en }270^\circ\\ \alpha = 194^\circ 2' 10{,}5"\)
5. \(8+7i\\ r = \sqrt{8^2+7^2} = \sqrt{113} \\ \alpha = tan^{-1}(\frac{7}{8}) \Leftrightarrow \alpha =41^\circ 11' 9{,}3"\text{ of } \alpha = 221^\circ 11' 9{,}3"\\8+7i\text{ ligt in kwadrant }1, \alpha \text{ ligt dus tussen }0^\circ \text{ en }90^\circ\\ \alpha = 41^\circ 11' 9{,}3"\)
6. \(-10-2i\\ r = \sqrt{(-10)^2+(-2)^2} = \sqrt{104} \\ \alpha = tan^{-1}(\frac{-2}{-10}) \Leftrightarrow \alpha =11^\circ 18' 35{,}8"\text{ of } \alpha = 191^\circ 18' 35{,}8"\\-10-2i\text{ ligt in kwadrant }3, \alpha \text{ ligt dus tussen }180^\circ \text{ en }270^\circ\\ \alpha = 191^\circ 18' 35{,}8"\)
7. \(-4+i\\ r = \sqrt{(-4)^2+1^2} = \sqrt{17} \\ \alpha = tan^{-1}(\frac{1}{-4}) \Leftrightarrow \alpha =165^\circ 57' 49{,}5"\text{ of } \alpha = 345^\circ 57' 49{,}5"\\-4+i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 165^\circ 57' 49{,}5"\)
8. \(2-4i\\ r = \sqrt{2^2+(-4)^2} = \sqrt{20} \\ \alpha = tan^{-1}(\frac{-4}{2}) \Leftrightarrow \alpha =116^\circ 33' 54{,}2"\text{ of } \alpha = 296^\circ 33' 54{,}2"\\2-4i\text{ ligt in kwadrant }4, \alpha \text{ ligt dus tussen }270^\circ \text{ en }360^\circ\\ \alpha = 296^\circ 33' 54{,}2"\)
9. \(-4+8i\\ r = \sqrt{(-4)^2+8^2} = \sqrt{80} \\ \alpha = tan^{-1}(\frac{8}{-4}) \Leftrightarrow \alpha =116^\circ 33' 54{,}2"\text{ of } \alpha = 296^\circ 33' 54{,}2"\\-4+8i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 116^\circ 33' 54{,}2"\)
10. \(4-i\\ r = \sqrt{4^2+(-1)^2} = \sqrt{17} \\ \alpha = tan^{-1}(\frac{-1}{4}) \Leftrightarrow \alpha =165^\circ 57' 49{,}5"\text{ of } \alpha = 345^\circ 57' 49{,}5"\\4-i\text{ ligt in kwadrant }4, \alpha \text{ ligt dus tussen }270^\circ \text{ en }360^\circ\\ \alpha = 345^\circ 57' 49{,}5"\)
11. \(1-8i\\ r = \sqrt{1^2+(-8)^2} = \sqrt{65} \\ \alpha = tan^{-1}(\frac{-8}{1}) \Leftrightarrow \alpha =97^\circ 7' 30{,}1"\text{ of } \alpha = 277^\circ 7' 30{,}1"\\1-8i\text{ ligt in kwadrant }4, \alpha \text{ ligt dus tussen }270^\circ \text{ en }360^\circ\\ \alpha = 277^\circ 7' 30{,}1"\)
12. \(-10+8i\\ r = \sqrt{(-10)^2+8^2} = \sqrt{164} \\ \alpha = tan^{-1}(\frac{8}{-10}) \Leftrightarrow \alpha =141^\circ 20' 24{,}7"\text{ of } \alpha = 321^\circ 20' 24{,}7"\\-10+8i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 141^\circ 20' 24{,}7"\)