Sendo Z1=4(cosπ+i senπ), Z2=3(cos 7π/4+i sen 7π/4) e Z3=2(cos 5π/6+i sen 5π/6), determine:
a)Z1. Z2
b)Z1 .Z3
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Fórmula de Euler:

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Escrevendo
na fórmula de Euler:

Portanto:
![z_{1}\cdot z_{2}=4e^{i\pi}\cdot3e^{i(7\pi/4)}=12e^{i\pi+i(7\pi/4)}=12e^{i[\pi+(7\pi/4)]}=12e^{i(11\pi/4)} z_{1}\cdot z_{2}=4e^{i\pi}\cdot3e^{i(7\pi/4)}=12e^{i\pi+i(7\pi/4)}=12e^{i[\pi+(7\pi/4)]}=12e^{i(11\pi/4)}](https://tex.z-dn.net/?f=z_%7B1%7D%5Ccdot+z_%7B2%7D%3D4e%5E%7Bi%5Cpi%7D%5Ccdot3e%5E%7Bi%287%5Cpi%2F4%29%7D%3D12e%5E%7Bi%5Cpi%2Bi%287%5Cpi%2F4%29%7D%3D12e%5E%7Bi%5B%5Cpi%2B%287%5Cpi%2F4%29%5D%7D%3D12e%5E%7Bi%2811%5Cpi%2F4%29%7D)
Reescrevendo o número (usando a fórmula), temos

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![z_{1}\cdot z_{3}=4e^{i\pi}\cdot2e^{i(5\pi/6)}=8e^{i\pi+i(5\pi/6)}=8e^{i[\pi+(5\pi/6)]}=8e^{i(11\pi/6)} z_{1}\cdot z_{3}=4e^{i\pi}\cdot2e^{i(5\pi/6)}=8e^{i\pi+i(5\pi/6)}=8e^{i[\pi+(5\pi/6)]}=8e^{i(11\pi/6)}](https://tex.z-dn.net/?f=z_%7B1%7D%5Ccdot+z_%7B3%7D%3D4e%5E%7Bi%5Cpi%7D%5Ccdot2e%5E%7Bi%285%5Cpi%2F6%29%7D%3D8e%5E%7Bi%5Cpi%2Bi%285%5Cpi%2F6%29%7D%3D8e%5E%7Bi%5B%5Cpi%2B%285%5Cpi%2F6%29%5D%7D%3D8e%5E%7Bi%2811%5Cpi%2F6%29%7D)
Portanto:

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Escrevendo
Portanto:
Reescrevendo o número (usando a fórmula), temos
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Portanto:
luanadonabella:
Obrigada !!!
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