Question

1. Aflati argumetul redus al numarului complex z=1-i2. Daza f:R-R, ,1. Aflati argumetul redus al numarului complex z=1-i
2. Daca f:R-R, , calculati (f cerculet f)(0)
3. Rezolvati in R ec: sinx-cosx=0
4.Det al cincilea termen al dezvoltarii binomiale
5. Daca A(2,0) B(0,3) si dreapta d are ec x-y+1=0, aflati coordonatele punctului C∈d pt care CA=CB
6. Aflati valoarea maxima a expresiei , X∈R

Answer 1

1)
[tex]z=1+(-1)i\\ arg(z)=\frac{3\pi}{2}+arctg\frac{|-1|}{1}=\frac{3\pi}{2}+\frac{\pi}{4}=\frac{7\pi}{4}[/tex]
2)(f₀f)(0)=f(f(0))=...
3)[tex]sinx-cosx=0\\ \sqrt{2}(sinx\cdot cos\frac{\pi}{4}-sin\frac{\pi}{4}\cdot cosx)=0\\ \sqrt{2}(sin(x-\frac{\pi}{4})=0=>sin(x-\frac{\pi}{4})=0\\ x-\frac{\pi}{4}=(-1)^karcsin0+k\pi,z\in Z\\ x=\frac{\pi}{4}+k\pi,k\in Z[/tex]
5)CA=CB=>[tex] \sqrt{(x-2)^2+(y-0)^2} = \sqrt{(x-0)^2+(y-3)^2} \\ (x-2)^2+(y-0)^2 = (x-0)^2+(y-3)^2\\ -4x+6y-5=0[/tex] Adiica punctul C se gaseste pe drepta de ecuatie :-4x+6y-5=0.