Bepaal modulus en argument

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Bepaal modulus en argument

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

Bepaal modulus en argument

Verbetersleutel

  1. \(10-9i\\ r = \sqrt{10^2+(-9)^2} = \sqrt{181} \\ \alpha = tan^{-1}(\frac{-9}{10}) \Leftrightarrow \alpha =138^\circ 0' 46"\text{ of } \alpha = 318^\circ 0' 46"\\10-9i\text{ ligt in kwadrant }4, \alpha \text{ ligt dus tussen }270^\circ \text{ en }360^\circ\\ \alpha = 318^\circ 0' 46"\)
  2. \(-2-8i\\ r = \sqrt{(-2)^2+(-8)^2} = \sqrt{68} \\ \alpha = tan^{-1}(\frac{-8}{-2}) \Leftrightarrow \alpha =75^\circ 57' 49{,}5"\text{ of } \alpha = 255^\circ 57' 49{,}5"\\-2-8i\text{ ligt in kwadrant }3, \alpha \text{ ligt dus tussen }180^\circ \text{ en }270^\circ\\ \alpha = 255^\circ 57' 49{,}5"\)
  3. \(-6+10i\\ r = \sqrt{(-6)^2+10^2} = \sqrt{136} \\ \alpha = tan^{-1}(\frac{10}{-6}) \Leftrightarrow \alpha =120^\circ 57' 49{,}5"\text{ of } \alpha = 300^\circ 57' 49{,}5"\\-6+10i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 120^\circ 57' 49{,}5"\)
  4. \(9+7i\\ r = \sqrt{9^2+7^2} = \sqrt{130} \\ \alpha = tan^{-1}(\frac{7}{9}) \Leftrightarrow \alpha =37^\circ 52' 29{,}9"\text{ of } \alpha = 217^\circ 52' 29{,}9"\\9+7i\text{ ligt in kwadrant }1, \alpha \text{ ligt dus tussen }0^\circ \text{ en }90^\circ\\ \alpha = 37^\circ 52' 29{,}9"\)
  5. \(-9+8i\\ r = \sqrt{(-9)^2+8^2} = \sqrt{145} \\ \alpha = tan^{-1}(\frac{8}{-9}) \Leftrightarrow \alpha =138^\circ 21' 59{,}3"\text{ of } \alpha = 318^\circ 21' 59{,}3"\\-9+8i\text{ ligt in kwadrant }2, \alpha \text{ ligt dus tussen }90^\circ \text{ en }180^\circ\\ \alpha = 138^\circ 21' 59{,}3"\)
  6. \(4+2i\\ r = \sqrt{4^2+2^2} = \sqrt{20} \\ \alpha = tan^{-1}(\frac{2}{4}) \Leftrightarrow \alpha =26^\circ 33' 54{,}2"\text{ of } \alpha = 206^\circ 33' 54{,}2"\\4+2i\text{ ligt in kwadrant }1, \alpha \text{ ligt dus tussen }0^\circ \text{ en }90^\circ\\ \alpha = 26^\circ 33' 54{,}2"\)
  7. \(8+i\\ r = \sqrt{8^2+1^2} = \sqrt{65} \\ \alpha = tan^{-1}(\frac{1}{8}) \Leftrightarrow \alpha =7^\circ 7' 30{,}1"\text{ of } \alpha = 187^\circ 7' 30{,}1"\\8+i\text{ ligt in kwadrant }1, \alpha \text{ ligt dus tussen }0^\circ \text{ en }90^\circ\\ \alpha = 7^\circ 7' 30{,}1"\)
  8. \(-5-3i\\ r = \sqrt{(-5)^2+(-3)^2} = \sqrt{34} \\ \alpha = tan^{-1}(\frac{-3}{-5}) \Leftrightarrow \alpha =30^\circ 57' 49{,}5"\text{ of } \alpha = 210^\circ 57' 49{,}5"\\-5-3i\text{ ligt in kwadrant }3, \alpha \text{ ligt dus tussen }180^\circ \text{ en }270^\circ\\ \alpha = 210^\circ 57' 49{,}5"\)
  9. \(5+8i\\ r = \sqrt{5^2+8^2} = \sqrt{89} \\ \alpha = tan^{-1}(\frac{8}{5}) \Leftrightarrow \alpha =57^\circ 59' 40{,}6"\text{ of } \alpha = 237^\circ 59' 40{,}6"\\5+8i\text{ ligt in kwadrant }1, \alpha \text{ ligt dus tussen }0^\circ \text{ en }90^\circ\\ \alpha = 57^\circ 59' 40{,}6"\)
  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. \(6+7i\\ r = \sqrt{6^2+7^2} = \sqrt{85} \\ \alpha = tan^{-1}(\frac{7}{6}) \Leftrightarrow \alpha =49^\circ 23' 55{,}3"\text{ of } \alpha = 229^\circ 23' 55{,}3"\\6+7i\text{ ligt in kwadrant }1, \alpha \text{ ligt dus tussen }0^\circ \text{ en }90^\circ\\ \alpha = 49^\circ 23' 55{,}3"\)
  12. \(5+5i\\ r = \sqrt{5^2+5^2} = \sqrt{50} \\ \alpha = tan^{-1}(\frac{5}{5}) \Leftrightarrow \alpha =45^\circ \text{ of } \alpha = 225^\circ \\5+5i\text{ ligt in kwadrant }1, \alpha \text{ ligt dus tussen }0^\circ \text{ en }90^\circ\\ \alpha = 45^\circ \)
Oefeningengenerator wiskundeoefeningen.be 2025-11-24 21:08:52
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