Question

Se y =2x,sendo x=1+i/1-i e i=√-1, o valor de ( x+y)elevado a 6 é,me ajudem por favor???
Mandem o cálculo.
Valendo 15 pontos!

Answer 1

Regra da aritmética complexa: $\frac{a+bi}{c+di}\:=\:\frac{\left(c-di\right)\left(a+bi\right)}{\left(c-di\right)\left(c+di\right)}\:=\:\frac{\left(ac+bd\right)+\left(bc-ad\right)i}{c^2+d^2}$

Resposta:

$x=\frac{1+i}{1-i}\\=\frac{\left(1\cdot \:1+1\cdot \left(-1\right)\right)+\left(1\cdot \:1-1\cdot \left(-1\right)\right)i}{1^2+\left(-1\right)^2}\\=\frac{2i}{2}\\=i$

$y=2x\\y=2i$

$(x+y)=(i+2i)=3i$