Question

Determine Z tal que: (1+i).Z=5-i

Answer 1

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


Multiplicando os dois lados da igualdade por $(1-i),$ temos

$(1-i)\,(1+i)\cdot z=(1-i)\,(5-i)\\ \\ (1^{2}-i^{2})\cdot z=5-i-5i+i^{2}\\ \\ (1-(-1))\cdot z=5-6i+(-1)\\ \\ (1+1)\cdot z=5-1-6i\\ \\ 2z=4-6i\\ \\ z=\dfrac{4-6i}{2}\\ \\ z=\dfrac{\diagup\!\!\!\! 2\,(2-3i)}{\diagup\!\!\!\! 2}\\ \\ z=2-3i$