Bepaal modulus en argument

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Bepaal modulus en argument

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

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Bepaal modulus en argument

Verbetersleutel

1. \(2-5i\\ r = \sqrt{2^2+(-5)^2} = \sqrt{29} \\ \alpha = tan^{-1}(\frac{-5}{2}) \Leftrightarrow \alpha =111^\circ 48' 5{,}1"\text{ of } \alpha = 291^\circ 48' 5{,}1"\\2-5i\text{ ligt in kwadrant }4, \alpha \text{ ligt dus tussen }270^\circ \text{ en }360^\circ\\ \alpha = 291^\circ 48' 5{,}1"\)
2. \(-6+3i\\ r = \sqrt{(-6)^2+3^2} = \sqrt{45} \\ \alpha = tan^{-1}(\frac{3}{-6}) \Leftrightarrow \alpha =153^\circ 26' 5{,}8"\text{ of } \alpha = 333^\circ 26' 5{,}8"\\-6+3i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 153^\circ 26' 5{,}8"\)
3. \(-3+4i\\ r = \sqrt{(-3)^2+4^2} = \sqrt{25} \\ \alpha = tan^{-1}(\frac{4}{-3}) \Leftrightarrow \alpha =126^\circ 52' 11{,}6"\text{ of } \alpha = 306^\circ 52' 11{,}6"\\-3+4i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 126^\circ 52' 11{,}6"\)
4. \(5+4i\\ r = \sqrt{5^2+4^2} = \sqrt{41} \\ \alpha = tan^{-1}(\frac{4}{5}) \Leftrightarrow \alpha =38^\circ 39' 35{,}3"\text{ of } \alpha = 218^\circ 39' 35{,}3"\\5+4i\text{ ligt in kwadrant }1, \alpha \text{ ligt dus tussen }0^\circ \text{ en }90^\circ\\ \alpha = 38^\circ 39' 35{,}3"\)
5. \(2-10i\\ r = \sqrt{2^2+(-10)^2} = \sqrt{104} \\ \alpha = tan^{-1}(\frac{-10}{2}) \Leftrightarrow \alpha =101^\circ 18' 35{,}8"\text{ of } \alpha = 281^\circ 18' 35{,}8"\\2-10i\text{ ligt in kwadrant }4, \alpha \text{ ligt dus tussen }270^\circ \text{ en }360^\circ\\ \alpha = 281^\circ 18' 35{,}8"\)
6. \(-2+8i\\ r = \sqrt{(-2)^2+8^2} = \sqrt{68} \\ \alpha = tan^{-1}(\frac{8}{-2}) \Leftrightarrow \alpha =104^\circ 2' 10{,}5"\text{ of } \alpha = 284^\circ 2' 10{,}5"\\-2+8i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 104^\circ 2' 10{,}5"\)
7. \(-3-8i\\ r = \sqrt{(-3)^2+(-8)^2} = \sqrt{73} \\ \alpha = tan^{-1}(\frac{-8}{-3}) \Leftrightarrow \alpha =69^\circ 26' 38{,}2"\text{ of } \alpha = 249^\circ 26' 38{,}2"\\-3-8i\text{ ligt in kwadrant }3, \alpha \text{ ligt dus tussen }180^\circ \text{ en }270^\circ\\ \alpha = 249^\circ 26' 38{,}2"\)
8. \(4-8i\\ r = \sqrt{4^2+(-8)^2} = \sqrt{80} \\ \alpha = tan^{-1}(\frac{-8}{4}) \Leftrightarrow \alpha =116^\circ 33' 54{,}2"\text{ of } \alpha = 296^\circ 33' 54{,}2"\\4-8i\text{ ligt in kwadrant }4, \alpha \text{ ligt dus tussen }270^\circ \text{ en }360^\circ\\ \alpha = 296^\circ 33' 54{,}2"\)
9. \(4+7i\\ r = \sqrt{4^2+7^2} = \sqrt{65} \\ \alpha = tan^{-1}(\frac{7}{4}) \Leftrightarrow \alpha =60^\circ 15' 18{,}4"\text{ of } \alpha = 240^\circ 15' 18{,}4"\\4+7i\text{ ligt in kwadrant }1, \alpha \text{ ligt dus tussen }0^\circ \text{ en }90^\circ\\ \alpha = 60^\circ 15' 18{,}4"\)
10. \(-8-i\\ r = \sqrt{(-8)^2+(-1)^2} = \sqrt{65} \\ \alpha = tan^{-1}(\frac{-1}{-8}) \Leftrightarrow \alpha =7^\circ 7' 30{,}1"\text{ of } \alpha = 187^\circ 7' 30{,}1"\\-8-i\text{ ligt in kwadrant }3, \alpha \text{ ligt dus tussen }180^\circ \text{ en }270^\circ\\ \alpha = 187^\circ 7' 30{,}1"\)
11. \(1-4i\\ r = \sqrt{1^2+(-4)^2} = \sqrt{17} \\ \alpha = tan^{-1}(\frac{-4}{1}) \Leftrightarrow \alpha =104^\circ 2' 10{,}5"\text{ of } \alpha = 284^\circ 2' 10{,}5"\\1-4i\text{ ligt in kwadrant }4, \alpha \text{ ligt dus tussen }270^\circ \text{ en }360^\circ\\ \alpha = 284^\circ 2' 10{,}5"\)
12. \(-10+6i\\ r = \sqrt{(-10)^2+6^2} = \sqrt{136} \\ \alpha = tan^{-1}(\frac{6}{-10}) \Leftrightarrow \alpha =149^\circ 2' 10{,}5"\text{ of } \alpha = 329^\circ 2' 10{,}5"\\-10+6i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 149^\circ 2' 10{,}5"\)