Question

Z= i^12 + (i^13-i^14)/(1+i^15)
Найдите действительную часть комплексного числа.

Answer 1

i²=-1

i³=-i

i⁴=1

i¹² = (i⁴)³ = 1³ = 1

i¹³ =  i¹²·i = 1·i = i

i¹⁴ = i¹³· i = i·i = - 1

i¹⁵ = i¹⁴·i=-1·i= - i

$z=i^{12}+\frac{i^{13}-i^{14}}{1+i^{15}}=1+\frac{i+1}{1-i}= 1+\frac{(i+1)(1+i)}{(1-i)(1+i)}= 1+\frac{i^2+2i+1}{1-i^2} =1+\frac{-1+2i+1}{1-(-1)} =1+\frac{2i}{2}=1+i$

Rez=1