Question

URGENTE O número z tal que iz= z -1+5i é: A) 3 + i B) 3 – i C) 3 -2i D) 3 + 2i E) -3 +

Answer 1

$iz=z-1+5i\\\\iz-z=-1+5i\\\\z(i-1)=-1+5i\\\\z(i-1)(i+1)=(-1+5i)(i+1)\\\\z(i^2-1^2)=-i-1+5i^2+5i\\\\z(-1-1)=-1+4i-5\\\\-2z=-6+4i\\\\z=3-2i$

Answer 2

Explicação passo-a-passo:

$\sf i\cdot z=z-1+5i$

$\sf z-i\cdot z=1-5i$

$\sf z\cdot(1-i)=1-5i$

$\sf z=\dfrac{1-5i}{1-i}\cdot\dfrac{1+i}{1+i}$

$\sf z=\dfrac{1-5i+i-5i^2}{1^2-i^2}$

$\sf z=\dfrac{1-5i+i-5\cdot(-1)}{1-(-1)}$

$\sf z=\dfrac{1-5i+i+5}{1+1}$

$\sf z=\dfrac{6-4i}{2}$

$\sf z=3-2i$

Letra C