Bepaal modulus en argument

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Bepaal modulus en argument

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

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Bepaal modulus en argument

Verbetersleutel

1. \(-1+8i\\ r = \sqrt{(-1)^2+8^2} = \sqrt{65} \\ \alpha = tan^{-1}(\frac{8}{-1}) \Leftrightarrow \alpha =97^\circ 7' 30{,}1"\text{ of } \alpha = 277^\circ 7' 30{,}1"\\-1+8i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 97^\circ 7' 30{,}1"\)
2. \(1+7i\\ r = \sqrt{1^2+7^2} = \sqrt{50} \\ \alpha = tan^{-1}(\frac{7}{1}) \Leftrightarrow \alpha =81^\circ 52' 11{,}6"\text{ of } \alpha = 261^\circ 52' 11{,}6"\\1+7i\text{ ligt in kwadrant }1, \alpha \text{ ligt dus tussen }0^\circ \text{ en }90^\circ\\ \alpha = 81^\circ 52' 11{,}6"\)
3. \(-7+3i\\ r = \sqrt{(-7)^2+3^2} = \sqrt{58} \\ \alpha = tan^{-1}(\frac{3}{-7}) \Leftrightarrow \alpha =156^\circ 48' 5{,}1"\text{ of } \alpha = 336^\circ 48' 5{,}1"\\-7+3i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 156^\circ 48' 5{,}1"\)
4. \(4+10i\\ r = \sqrt{4^2+10^2} = \sqrt{116} \\ \alpha = tan^{-1}(\frac{10}{4}) \Leftrightarrow \alpha =68^\circ 11' 54{,}9"\text{ of } \alpha = 248^\circ 11' 54{,}9"\\4+10i\text{ ligt in kwadrant }1, \alpha \text{ ligt dus tussen }0^\circ \text{ en }90^\circ\\ \alpha = 68^\circ 11' 54{,}9"\)
5. \(-10+3i\\ r = \sqrt{(-10)^2+3^2} = \sqrt{109} \\ \alpha = tan^{-1}(\frac{3}{-10}) \Leftrightarrow \alpha =163^\circ 18' 2{,}7"\text{ of } \alpha = 343^\circ 18' 2{,}7"\\-10+3i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 163^\circ 18' 2{,}7"\)
6. \(9+4i\\ r = \sqrt{9^2+4^2} = \sqrt{97} \\ \alpha = tan^{-1}(\frac{4}{9}) \Leftrightarrow \alpha =23^\circ 57' 45"\text{ of } \alpha = 203^\circ 57' 45"\\9+4i\text{ ligt in kwadrant }1, \alpha \text{ ligt dus tussen }0^\circ \text{ en }90^\circ\\ \alpha = 23^\circ 57' 45"\)
7. \(10+7i\\ r = \sqrt{10^2+7^2} = \sqrt{149} \\ \alpha = tan^{-1}(\frac{7}{10}) \Leftrightarrow \alpha =34^\circ 59' 31{,}3"\text{ of } \alpha = 214^\circ 59' 31{,}3"\\10+7i\text{ ligt in kwadrant }1, \alpha \text{ ligt dus tussen }0^\circ \text{ en }90^\circ\\ \alpha = 34^\circ 59' 31{,}3"\)
8. \(-3-9i\\ r = \sqrt{(-3)^2+(-9)^2} = \sqrt{90} \\ \alpha = tan^{-1}(\frac{-9}{-3}) \Leftrightarrow \alpha =71^\circ 33' 54{,}2"\text{ of } \alpha = 251^\circ 33' 54{,}2"\\-3-9i\text{ ligt in kwadrant }3, \alpha \text{ ligt dus tussen }180^\circ \text{ en }270^\circ\\ \alpha = 251^\circ 33' 54{,}2"\)
9. \(6-9i\\ r = \sqrt{6^2+(-9)^2} = \sqrt{117} \\ \alpha = tan^{-1}(\frac{-9}{6}) \Leftrightarrow \alpha =123^\circ 41' 24{,}2"\text{ of } \alpha = 303^\circ 41' 24{,}2"\\6-9i\text{ ligt in kwadrant }4, \alpha \text{ ligt dus tussen }270^\circ \text{ en }360^\circ\\ \alpha = 303^\circ 41' 24{,}2"\)
10. \(5+5i\\ r = \sqrt{5^2+5^2} = \sqrt{50} \\ \alpha = tan^{-1}(\frac{5}{5}) \Leftrightarrow \alpha =45^\circ \text{ of } \alpha = 225^\circ \\5+5i\text{ ligt in kwadrant }1, \alpha \text{ ligt dus tussen }0^\circ \text{ en }90^\circ\\ \alpha = 45^\circ \)
11. \(10-9i\\ r = \sqrt{10^2+(-9)^2} = \sqrt{181} \\ \alpha = tan^{-1}(\frac{-9}{10}) \Leftrightarrow \alpha =138^\circ 0' 46"\text{ of } \alpha = 318^\circ 0' 46"\\10-9i\text{ ligt in kwadrant }4, \alpha \text{ ligt dus tussen }270^\circ \text{ en }360^\circ\\ \alpha = 318^\circ 0' 46"\)
12. \(-8+3i\\ r = \sqrt{(-8)^2+3^2} = \sqrt{73} \\ \alpha = tan^{-1}(\frac{3}{-8}) \Leftrightarrow \alpha =159^\circ 26' 38{,}2"\text{ of } \alpha = 339^\circ 26' 38{,}2"\\-8+3i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 159^\circ 26' 38{,}2"\)