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Multiplying and dividing complex numbers

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Lessons
  1. Multiplying complex numbers
    1. (3+i)×(1+3i)(3+i)\times(1+3i)
    2. (1−2i)×(−2+32i) (1-\sqrt{2}i)\times(-2+3\sqrt{2}i)
    3. (6−5i)×(6+5i)(6-5i)\times(6+5i)
  2. Dividing complex numbers
    1. (1+2i)÷(3−i) (1+2i)\div(3-i)
    2. 5−5i−4+5i\frac{5-\sqrt{5}i}{-4+\sqrt{5}i}
    3. 2−3i3i+2 \frac{2-3i}{3i+2}
  3. Given that z=5+6i z=5+6i , determine z‾⋅z\overline{z}\cdot z
    1. Given that w=2−5iw=2-5i , z=3+6iz=3+6i determine w⋅z‾w \cdot \overline{z}