18/5=3 и ост. 3
Потому что 5*3=15, а 18-15=3
(1+t²)²=(1)²+2*1*t²+(t²)²=1+2t²+t⁴
А) z1 = |1-2i| =
![\sqrt{1^2+(-2)^2}](https://tex.z-dn.net/?f=++%5Csqrt%7B1%5E2%2B%28-2%29%5E2%7D+)
=
![\sqrt{5}](https://tex.z-dn.net/?f=+%5Csqrt%7B5%7D+)
z2 = |4-i| =
![\sqrt{4^2+(-1)^2}](https://tex.z-dn.net/?f=+%5Csqrt%7B4%5E2%2B%28-1%29%5E2%7D+)
=
![\sqrt{17}](https://tex.z-dn.net/?f=+%5Csqrt%7B17%7D+)
б)|z1+z2| = |(1-2i)+(4-i)| = |5-3i| =
![\sqrt{5^2+(-3)^2}](https://tex.z-dn.net/?f=+%5Csqrt%7B5%5E2%2B%28-3%29%5E2%7D+)
=
![\sqrt{34}](https://tex.z-dn.net/?f=+%5Csqrt%7B34%7D+)
в)|z1-z2| = |(1-2i)-(4-i)| = |-3-i| =
![\sqrt{(-3)^2+(-1)^2}](https://tex.z-dn.net/?f=+%5Csqrt%7B%28-3%29%5E2%2B%28-1%29%5E2%7D+)
=
![\sqrt{10}](https://tex.z-dn.net/?f=+%5Csqrt%7B10%7D+)
г)|z1*z2| = |(1-2i)(4-i)| = |4-i-8i+2i^2| = |4 -9i -2| = |2-9i| =
![\sqrt{2^2+(-9)^2}](https://tex.z-dn.net/?f=+%5Csqrt%7B2%5E2%2B%28-9%29%5E2%7D+)
=
д)|z1:z2| = |
![\frac{1-2i}{4-i}](https://tex.z-dn.net/?f=+%5Cfrac%7B1-2i%7D%7B4-i%7D+)
| = |
![\frac{1-2i}{4-i} * \frac{4+i}{4+i}](https://tex.z-dn.net/?f=+%5Cfrac%7B1-2i%7D%7B4-i%7D+%2A+%5Cfrac%7B4%2Bi%7D%7B4%2Bi%7D+)
| = |
![\frac{(1-2i)(4+i)}{16-i^2}| = |\frac{6-7i}{17}| = |\frac{6}{17}- \frac{7}{17}i](https://tex.z-dn.net/?f=+%5Cfrac%7B%281-2i%29%284%2Bi%29%7D%7B16-i%5E2%7D%7C+%3D+%7C%5Cfrac%7B6-7i%7D%7B17%7D%7C+%3D+%7C%5Cfrac%7B6%7D%7B17%7D-+%5Cfrac%7B7%7D%7B17%7Di)
| =
![\sqrt{(\frac{6}{17})^2+ (\frac{7}{17})^2} = \sqrt{ \frac{36}{289}+ \frac{49}{289}} = \frac{ \sqrt{85}}{17}](https://tex.z-dn.net/?f=+%5Csqrt%7B%28%5Cfrac%7B6%7D%7B17%7D%29%5E2%2B+%28%5Cfrac%7B7%7D%7B17%7D%29%5E2%7D+%3D++%5Csqrt%7B+%5Cfrac%7B36%7D%7B289%7D%2B+%5Cfrac%7B49%7D%7B289%7D%7D+++%3D+++%5Cfrac%7B+%5Csqrt%7B85%7D%7D%7B17%7D+)
Решение, раскрытие скобок и формула квадратного уравнения
Log(3)2x0.25 = log(3)0.5
дальше идёт число за нулём так что оставь так