Question

1)calcule a norma e escreva na forma algebrica dos complexos abaixo a)z=1+2i b)(0,-3i)
2)a forma z=a+bi de z=1+2i/1-i

Answer 1

Explicação passo-a-passo:

1.

a)

• Norma: $\sf ||Z||=|Z|^2=a^2+b^2$

$\sf Z=1+2i~\rightarrow~a=1,~b=2$

• $\sf ||Z||=1^2+2^2$

$\sf ||Z||=1+4$

$\sf ||Z||=5$

b) $\sf (0,-3)$

• Forma algébrica: $\sf Z=a+bi$

$\sf Z=-3i$

• Norma:

$\sf ||Z||=0^2+(-3)^2$

$\sf ||Z||=0+9$

$\sf ||Z||=9$

2.

$\sf Z=\dfrac{1+2i}{1-i}$

$\sf Z=\dfrac{1+2i}{1-i}\cdot\dfrac{1+i}{1+i}$

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

$\sf Z=\dfrac{1+3i+2\cdot(-1)}{1-(-1)}$

$\sf Z=\dfrac{1+3i-2}{1+1}$

$\sf Z=\dfrac{-1+3i}{2}$

$\sf Z=\dfrac{-1}{2}+\dfrac{3i}{2}$