Bepaal modulus en argument

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Bepaal modulus en argument

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

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Bepaal modulus en argument

Verbetersleutel

1. \(1+8i\\ r = \sqrt{1^2+8^2} = \sqrt{65} \\ \alpha = tan^{-1}(\frac{8}{1}) \Leftrightarrow \alpha =82^\circ 52' 29{,}9"\text{ of } \alpha = 262^\circ 52' 29{,}9"\\1+8i\text{ ligt in kwadrant }1, \alpha \text{ ligt dus tussen }0^\circ \text{ en }90^\circ\\ \alpha = 82^\circ 52' 29{,}9"\)
2. \(-3+7i\\ r = \sqrt{(-3)^2+7^2} = \sqrt{58} \\ \alpha = tan^{-1}(\frac{7}{-3}) \Leftrightarrow \alpha =113^\circ 11' 54{,}9"\text{ of } \alpha = 293^\circ 11' 54{,}9"\\-3+7i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 113^\circ 11' 54{,}9"\)
3. \(-1+5i\\ r = \sqrt{(-1)^2+5^2} = \sqrt{26} \\ \alpha = tan^{-1}(\frac{5}{-1}) \Leftrightarrow \alpha =101^\circ 18' 35{,}8"\text{ of } \alpha = 281^\circ 18' 35{,}8"\\-1+5i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 101^\circ 18' 35{,}8"\)
4. \(-7+3i\\ r = \sqrt{(-7)^2+3^2} = \sqrt{58} \\ \alpha = tan^{-1}(\frac{3}{-7}) \Leftrightarrow \alpha =156^\circ 48' 5{,}1"\text{ of } \alpha = 336^\circ 48' 5{,}1"\\-7+3i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 156^\circ 48' 5{,}1"\)
5. \(5+3i\\ r = \sqrt{5^2+3^2} = \sqrt{34} \\ \alpha = tan^{-1}(\frac{3}{5}) \Leftrightarrow \alpha =30^\circ 57' 49{,}5"\text{ of } \alpha = 210^\circ 57' 49{,}5"\\5+3i\text{ ligt in kwadrant }1, \alpha \text{ ligt dus tussen }0^\circ \text{ en }90^\circ\\ \alpha = 30^\circ 57' 49{,}5"\)
6. \(1+3i\\ r = \sqrt{1^2+3^2} = \sqrt{10} \\ \alpha = tan^{-1}(\frac{3}{1}) \Leftrightarrow \alpha =71^\circ 33' 54{,}2"\text{ of } \alpha = 251^\circ 33' 54{,}2"\\1+3i\text{ ligt in kwadrant }1, \alpha \text{ ligt dus tussen }0^\circ \text{ en }90^\circ\\ \alpha = 71^\circ 33' 54{,}2"\)
7. \(-4+6i\\ r = \sqrt{(-4)^2+6^2} = \sqrt{52} \\ \alpha = tan^{-1}(\frac{6}{-4}) \Leftrightarrow \alpha =123^\circ 41' 24{,}2"\text{ of } \alpha = 303^\circ 41' 24{,}2"\\-4+6i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 123^\circ 41' 24{,}2"\)
8. \(-8-8i\\ r = \sqrt{(-8)^2+(-8)^2} = \sqrt{128} \\ \alpha = tan^{-1}(\frac{-8}{-8}) \Leftrightarrow \alpha =45^\circ \text{ of } \alpha = 225^\circ \\-8-8i\text{ ligt in kwadrant }3, \alpha \text{ ligt dus tussen }180^\circ \text{ en }270^\circ\\ \alpha = 225^\circ \)
9. \(10+3i\\ r = \sqrt{10^2+3^2} = \sqrt{109} \\ \alpha = tan^{-1}(\frac{3}{10}) \Leftrightarrow \alpha =16^\circ 41' 57{,}3"\text{ of } \alpha = 196^\circ 41' 57{,}3"\\10+3i\text{ ligt in kwadrant }1, \alpha \text{ ligt dus tussen }0^\circ \text{ en }90^\circ\\ \alpha = 16^\circ 41' 57{,}3"\)
10. \(-9+8i\\ r = \sqrt{(-9)^2+8^2} = \sqrt{145} \\ \alpha = tan^{-1}(\frac{8}{-9}) \Leftrightarrow \alpha =138^\circ 21' 59{,}3"\text{ of } \alpha = 318^\circ 21' 59{,}3"\\-9+8i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 138^\circ 21' 59{,}3"\)
11. \(7-4i\\ r = \sqrt{7^2+(-4)^2} = \sqrt{65} \\ \alpha = tan^{-1}(\frac{-4}{7}) \Leftrightarrow \alpha =150^\circ 15' 18{,}4"\text{ of } \alpha = 330^\circ 15' 18{,}4"\\7-4i\text{ ligt in kwadrant }4, \alpha \text{ ligt dus tussen }270^\circ \text{ en }360^\circ\\ \alpha = 330^\circ 15' 18{,}4"\)
12. \(-8+6i\\ r = \sqrt{(-8)^2+6^2} = \sqrt{100} \\ \alpha = tan^{-1}(\frac{6}{-8}) \Leftrightarrow \alpha =143^\circ 7' 48{,}4"\text{ of } \alpha = 323^\circ 7' 48{,}4"\\-8+6i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 143^\circ 7' 48{,}4"\)