Question

Calcule i¹⁰³⁵ e b(2-2i)²

Answer 1

$\Large\boxed{\begin{array}{l}\rm a)~i^{1035}\\\sf 1035\,\,\,|\underline{4~~~~}\\\!\!\!\!-\underline{\sf~8~~~~~}\,\sf 258\\\sf23\\\!\!\!\!\!-\underline{\sf20}\\\sf35\\\!\!\!\!\!-\underline{\sf32}\\\sf3\\\sf i^{1035}=i^{3}=-i\end{array}}$

$\Large\boxed{\begin{array}{l}\sf (2-2i)^2=(2)^2-2\cdot2\cdot2i+(2i)^2\\\sf (2-2i)^2=4-8i+4i^2\\\sf (2-2i)^2=\backslash\!\!\!4-8i-\backslash\!\!\!\!4=-8i\end{array}}$