Question

Números complexos, resolva as questões:

Se z1=1-3i e z2=2+5i, determine:

A) |z1+z2|

B) |z1.z2|

C) |z1|+|z2|

D) |z1-z2|

Answer 1

Explicação passo-a-passo:

a) $|z_1+z_2|=|1-3i+2+5i|$

$|z_1+z_2|=|3+2i|$

$|z_1+z_2|=\sqrt{3^2+2^2}$

$|z_1+z_2|=\sqrt{9+4}$

$|z_1+z_2|=\sqrt{13}$

b) $|z_1\cdot z_2|=|(1-3i)\cdot(2+5i)|$

$|z_1\cdot z_2|=|2+5i-6i-15i^2|$

$|z_1\cdot z_2|=|2+5i-6i+15|$

$|z_1\cdot z_2|=|17-i|$

$|z_1\cdot z_2|=\sqrt{17^2+(-1)^2}$

$|z_1\cdot z_2|=\sqrt{289+1}$

$|z_1\cdot z_2|=\sqrt{290}$

c) $|z_1|+|z_2|=|1-3i|+|2+5i|$

$|z_1|+|z_2|=\sqrt{1^2+(-3)^2}+\sqrt{2^2+5^2}$

$|z_1|+|z_2|=\sqrt{1+9}+\sqrt{4+25}$

$|z_1|+|z_2|=\sqrt{10}+\sqrt{29}$

d) $|z_1-z_2|=|1-3i-(2+5i)|$

$|z_1-z_2|=|1-3i-2-5i|$

$|z_1-z_2|=|-1-8i|$

$|z_1-z_2|=\sqrt{(-1)^2+(-8)^2}$

$|z_1-z_2|=\sqrt{1+64}$

$|z_1-z_2|=\sqrt{65}$