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1.
![frac{3+i}{2-8i} = frac{(3+i)(1+4i)}{2(1 -16i^2)} = frac{3+13i+4i^2}{2*(1+16)} = frac{3-4+13i}{34} = -frac{1}{34} + frac{13}{34} i frac{3+i}{2-8i} = frac{(3+i)(1+4i)}{2(1 -16i^2)} = frac{3+13i+4i^2}{2*(1+16)} = frac{3-4+13i}{34} = -frac{1}{34} + frac{13}{34} i](https://tex.z-dn.net/?f=+frac%7B3%2Bi%7D%7B2-8i%7D+%3D+frac%7B%283%2Bi%29%281%2B4i%29%7D%7B2%281+-16i%5E2%29%7D+%3D+frac%7B3%2B13i%2B4i%5E2%7D%7B2%2A%281%2B16%29%7D+%3D+frac%7B3-4%2B13i%7D%7B34%7D+%3D+-frac%7B1%7D%7B34%7D+%2B+frac%7B13%7D%7B34%7D+i)
![frac{1+2i}{-4+2i}= frac{(1+2i)(-2-i)}{2(-2+i)(-2-i)} = frac{-2-5i-2i^2}{2(4-i^2)} = frac{-2+2-5i}{2(4+1)} = frac{-5i}{2*5} =- frac{1}{2} i frac{1+2i}{-4+2i}= frac{(1+2i)(-2-i)}{2(-2+i)(-2-i)} = frac{-2-5i-2i^2}{2(4-i^2)} = frac{-2+2-5i}{2(4+1)} = frac{-5i}{2*5} =- frac{1}{2} i](https://tex.z-dn.net/?f=+frac%7B1%2B2i%7D%7B-4%2B2i%7D%3D+frac%7B%281%2B2i%29%28-2-i%29%7D%7B2%28-2%2Bi%29%28-2-i%29%7D++%3D+frac%7B-2-5i-2i%5E2%7D%7B2%284-i%5E2%29%7D+%3D+frac%7B-2%2B2-5i%7D%7B2%284%2B1%29%7D+%3D+frac%7B-5i%7D%7B2%2A5%7D+%3D-+frac%7B1%7D%7B2%7D+i)
2.
![|-2+2 sqrt{3} i| = sqrt{4+4*3} = sqrt{16} =4\
|3-4 sqrt{5} i|= sqrt{9+16*5} = sqrt{89} |-2+2 sqrt{3} i| = sqrt{4+4*3} = sqrt{16} =4\
|3-4 sqrt{5} i|= sqrt{9+16*5} = sqrt{89}](https://tex.z-dn.net/?f=%7C-2%2B2+sqrt%7B3%7D+i%7C+%3D++sqrt%7B4%2B4%2A3%7D+%3D+sqrt%7B16%7D+%3D4%5C%0A%7C3-4+sqrt%7B5%7D+i%7C%3D+sqrt%7B9%2B16%2A5%7D+%3D+sqrt%7B89%7D+)
3.
![(6-2i)(3-4i)=18-6i-24i+8i^2=18-8-30i=10-30i (6-2i)(3-4i)=18-6i-24i+8i^2=18-8-30i=10-30i](https://tex.z-dn.net/?f=%286-2i%29%283-4i%29%3D18-6i-24i%2B8i%5E2%3D18-8-30i%3D10-30i)
![(1+2i)(3+i)=3+6i+i+2i^2=3-2+7i=1+7i (1+2i)(3+i)=3+6i+i+2i^2=3-2+7i=1+7i](https://tex.z-dn.net/?f=%281%2B2i%29%283%2Bi%29%3D3%2B6i%2Bi%2B2i%5E2%3D3-2%2B7i%3D1%2B7i)
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