Question

1)Demonstrati ca:a)$\frac{1+3i}{1-3i} + \frac{1-3i}{1+3i}$∈R
b)$(1+i \sqrt{3}) ^{3}$∈Z
c)$(1-i) ^{24}$∈R
2)Determinati partea imaginara a numarului $z= \frac{2+3i}{3-2i}$
3)Calculati :a)$i*i ^{2} *....*i ^{10}$;b)$1+i+i ^{2} +....+i ^{10}$
4)Calculati:a)$( \frac{(1-2i)(3i-1)}{5} ) ^{4}$;b)$( \frac{1-i}{ \sqrt{2} } ) ^{24}$
5)Se considera a∈R si numarul complex z=$\frac{a+2i}{2+ai}$.Determinati a pentru care z∈R.

Answer 1

Am atasat rezolvarea.