Question

Помогите решить пожалуйста,тема: действия с комплексными числами

Answer 1

$1)(frac{1}{1-i})^{2} = frac{1}{(1-i)(1-i)} = frac{1}{1-i-i+i^{2}} = frac{1}{-2i} = -frac{1}{2}i\\ 2) frac{2i-3}{1+i} + frac{3i+4}{2-i} = frac{(2i-3)(2-i)+(3i+4)(1+i)}{(1+i)(2-i)} = \\ = frac{4i-2i^{2}-6+3i+3i+3i^{2}+4+4i}{2-i+2i-i^{2}} = frac{14i-3}{i+3} = frac{14(i-3)(i-3)}{(i+3)(i-3)} = frac{14(i^{2}-3i-3i+9)}{-10} = \\ frac{28(4-3i)}{-10} = -2.8(4-3i) = 8.4i-11.2$
$3) (2+xi)^{2}=-46+yi\ (2+xi)(2+xi)=-46+yi\ 4+2xi+2xi+x^{2}i^{2}=-46+yi\ 4-x^{2}+4xi = -46+yi\ left { {{4-x^{2}=-46} atop {4x=y}} right.\ -x^{2}=-50\ x^{2}=50\ x = sqrt{50} = 5sqrt{2}\ y = 4x = 20sqrt{2}$