Question

MATEMÁTICA
porfavor só responda se souber

1. usando Z1=3+4i e Z2=4-3i calcule
a) Z1+Z2
b)Z1-Z2
c)Z1.Z2
d)Z1%Z2 ​

Answer 1

Explicação passo-a-passo:

a)

$\sf Z_1+Z_2=3+4i+4-3i$

$\sf Z_1+Z_2=3+4+4i-3i$

$\sf \red{Z_1+Z_2=7+i}$

b)

$\sf Z_1-Z_2=3+4i-(4-3i)$

$\sf Z_1-Z_2=3+4i-4+3i$

$\sf Z_1-Z_2=3-4+4i+3i$

$\sf \red{Z_1-Z_2=-1+7i}$

c)

$\sf Z_1\cdot Z_2=(3+4i)\cdot(4-3i)$

$\sf Z_1\cdot Z_2=12-9i+16i-12i^2$

$\sf Z_1\cdot Z_2=12-9i+16i-12\cdot(-1)$

$\sf Z_1\cdot Z_2=12-9i+16i+12$

$\sf Z_1\cdot Z_2=12+12-9i+16i$

$\sf \red{Z_1\cdot Z_2=24+7i}$

d)

$\sf \dfrac{Z_1}{Z_2}=\dfrac{3+4i}{4-3i}$

$\sf \dfrac{Z_1}{Z_2}=\dfrac{3+4i}{4-3i}\cdot\dfrac{4+3i}{4+3i}$

$\sf \dfrac{Z_1}{Z_2}=\dfrac{12+9i+16i+12i^2}{4^2-(3i)^2}$

$\sf \dfrac{Z_1}{Z_2}=\dfrac{12+9i+16i+12i\cdot(-1)}{4^2-9i^2}$

$\sf \dfrac{Z_1}{Z_2}=\dfrac{12+9i+16i-12}{16-9\cdot(-1)}$

$\sf \dfrac{Z_1}{Z_2}=\dfrac{12-12+9i+16i}{16+9}$

$\sf \dfrac{Z_1}{Z_2}=\dfrac{25i}{25}$

$\sf \red{\dfrac{Z_1}{Z_2}=i}$