Bepaal modulus en argument

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Bepaal modulus en argument

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

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Bepaal modulus en argument

Verbetersleutel

1. \(3-2i\\ r = \sqrt{3^2+(-2)^2} = \sqrt{13} \\ \alpha = tan^{-1}(\frac{-2}{3}) \Leftrightarrow \alpha =146^\circ 18' 35{,}8"\text{ of } \alpha = 326^\circ 18' 35{,}8"\\3-2i\text{ ligt in kwadrant }4, \alpha \text{ ligt dus tussen }270^\circ \text{ en }360^\circ\\ \alpha = 326^\circ 18' 35{,}8"\)
2. \(4+5i\\ r = \sqrt{4^2+5^2} = \sqrt{41} \\ \alpha = tan^{-1}(\frac{5}{4}) \Leftrightarrow \alpha =51^\circ 20' 24{,}7"\text{ of } \alpha = 231^\circ 20' 24{,}7"\\4+5i\text{ ligt in kwadrant }1, \alpha \text{ ligt dus tussen }0^\circ \text{ en }90^\circ\\ \alpha = 51^\circ 20' 24{,}7"\)
3. \(-8+4i\\ r = \sqrt{(-8)^2+4^2} = \sqrt{80} \\ \alpha = tan^{-1}(\frac{4}{-8}) \Leftrightarrow \alpha =153^\circ 26' 5{,}8"\text{ of } \alpha = 333^\circ 26' 5{,}8"\\-8+4i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 153^\circ 26' 5{,}8"\)
4. \(-3-9i\\ r = \sqrt{(-3)^2+(-9)^2} = \sqrt{90} \\ \alpha = tan^{-1}(\frac{-9}{-3}) \Leftrightarrow \alpha =71^\circ 33' 54{,}2"\text{ of } \alpha = 251^\circ 33' 54{,}2"\\-3-9i\text{ ligt in kwadrant }3, \alpha \text{ ligt dus tussen }180^\circ \text{ en }270^\circ\\ \alpha = 251^\circ 33' 54{,}2"\)
5. \(1+7i\\ r = \sqrt{1^2+7^2} = \sqrt{50} \\ \alpha = tan^{-1}(\frac{7}{1}) \Leftrightarrow \alpha =81^\circ 52' 11{,}6"\text{ of } \alpha = 261^\circ 52' 11{,}6"\\1+7i\text{ ligt in kwadrant }1, \alpha \text{ ligt dus tussen }0^\circ \text{ en }90^\circ\\ \alpha = 81^\circ 52' 11{,}6"\)
6. \(1+8i\\ r = \sqrt{1^2+8^2} = \sqrt{65} \\ \alpha = tan^{-1}(\frac{8}{1}) \Leftrightarrow \alpha =82^\circ 52' 29{,}9"\text{ of } \alpha = 262^\circ 52' 29{,}9"\\1+8i\text{ ligt in kwadrant }1, \alpha \text{ ligt dus tussen }0^\circ \text{ en }90^\circ\\ \alpha = 82^\circ 52' 29{,}9"\)
7. \(-10+3i\\ r = \sqrt{(-10)^2+3^2} = \sqrt{109} \\ \alpha = tan^{-1}(\frac{3}{-10}) \Leftrightarrow \alpha =163^\circ 18' 2{,}7"\text{ of } \alpha = 343^\circ 18' 2{,}7"\\-10+3i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 163^\circ 18' 2{,}7"\)
8. \(3-4i\\ r = \sqrt{3^2+(-4)^2} = \sqrt{25} \\ \alpha = tan^{-1}(\frac{-4}{3}) \Leftrightarrow \alpha =126^\circ 52' 11{,}6"\text{ of } \alpha = 306^\circ 52' 11{,}6"\\3-4i\text{ ligt in kwadrant }4, \alpha \text{ ligt dus tussen }270^\circ \text{ en }360^\circ\\ \alpha = 306^\circ 52' 11{,}6"\)
9. \(-3+8i\\ r = \sqrt{(-3)^2+8^2} = \sqrt{73} \\ \alpha = tan^{-1}(\frac{8}{-3}) \Leftrightarrow \alpha =110^\circ 33' 21{,}8"\text{ of } \alpha = 290^\circ 33' 21{,}8"\\-3+8i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 110^\circ 33' 21{,}8"\)
10. \(6-10i\\ r = \sqrt{6^2+(-10)^2} = \sqrt{136} \\ \alpha = tan^{-1}(\frac{-10}{6}) \Leftrightarrow \alpha =120^\circ 57' 49{,}5"\text{ of } \alpha = 300^\circ 57' 49{,}5"\\6-10i\text{ ligt in kwadrant }4, \alpha \text{ ligt dus tussen }270^\circ \text{ en }360^\circ\\ \alpha = 300^\circ 57' 49{,}5"\)
11. \(7+2i\\ r = \sqrt{7^2+2^2} = \sqrt{53} \\ \alpha = tan^{-1}(\frac{2}{7}) \Leftrightarrow \alpha =15^\circ 56' 43{,}4"\text{ of } \alpha = 195^\circ 56' 43{,}4"\\7+2i\text{ ligt in kwadrant }1, \alpha \text{ ligt dus tussen }0^\circ \text{ en }90^\circ\\ \alpha = 15^\circ 56' 43{,}4"\)
12. \(5+2i\\ r = \sqrt{5^2+2^2} = \sqrt{29} \\ \alpha = tan^{-1}(\frac{2}{5}) \Leftrightarrow \alpha =21^\circ 48' 5{,}1"\text{ of } \alpha = 201^\circ 48' 5{,}1"\\5+2i\text{ ligt in kwadrant }1, \alpha \text{ ligt dus tussen }0^\circ \text{ en }90^\circ\\ \alpha = 21^\circ 48' 5{,}1"\)