Question

20 баллов двю.Срочноо.
(-5+5i)в 3 степени=?
(2+i)/(-3+i)=?
(2+i)(-3+i)=?

Answer 1

$1)quad (-5+5i)^3=(-5(1-i))^3=(-5)^3(1-i)^3=\\=-125(1-3i+3i^2-i^3)=-125(1-3i-3+i)=\\=-125(-2-2i)=-250(1+i)\\star ; ; i^2=-1; ,; ; i^3=i^2cdot i=-1cdot i=-i; ; star \\2) frac{2+i}{-3+i} = frac{(2+i)(3+i)}{-(3-i)(3+i)} = frac{6+5i+i^2}{9-i^2} = frac{5+5i}{9+1} = frac{5(1+i)}{10} = frac{1+i}{2}= frac{1}{2} +frac{1}{2}i$

$3)quad (2+i)(-3+i)=-6+2i-3i+i^2=-6-i-1=-7-i$