Multiplying and dividing complex numbers

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Examples
Lessons
1. Multiplying complex numbers
1. $(3+i)\times(1+3i)$
2. $(1-\sqrt{2}i)\times(-2+3\sqrt{2}i)$
3. $(6-5i)\times(6+5i)$
2. Dividing complex numbers
1. $(1+2i)\div(3-i)$
2. $\frac{5-\sqrt{5}i}{-4+\sqrt{5}i}$
3. $\frac{2-3i}{3i+2}$
3. Given that $z=5+6i$, determine $\overline{z}\cdot z$
1. Given that $w=2-5i$, $z=3+6i$ determine $w \cdot \overline{z}$
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