A Nagwa usa cookies para garantir que vocΓͺ tenha a melhor experiΓͺncia em nosso site. Saiba mais sobre nossa PolΓ­tica de privacidade.

Aula: Convertendo as Diferentes Formas do Número Complexo

Atividade • 17 Questões

Q1:

Coloque 𝑧 = 4 √ 3 ο€Ό 5 πœ‹ 6 βˆ’ 𝑖 5 πœ‹ 6  c o s s e n na forma exponencial.

  • A 4 √ 3 𝑒 7 πœ‹ 6 𝑖
  • B √ 3 1 2 𝑒 7 πœ‹ 6 𝑖
  • C 4 √ 3 𝑒 5 πœ‹ 6 𝑖
  • D 𝑒 5 πœ‹ 6 𝑖
  • E 𝑒 7 πœ‹ 6 𝑖

Q2:

Coloque 𝑧 = βˆ’ 4 √ 3 ο€Ό 5 πœ‹ 6 + 𝑖 5 πœ‹ 6  s e n c o s na forma exponencial.

  • A 4 √ 3 𝑒 2 πœ‹ 3 𝑖
  • B 1 2 𝑒 2 πœ‹ 3 𝑖
  • C 4 √ 3 𝑒 5 πœ‹ 6 𝑖
  • D βˆ’ 4 √ 3 𝑒 2 πœ‹ 3 𝑖
  • E 𝑒 2 πœ‹ 3 𝑖

Q3:

Expresse o nΓΊmero complexo 𝑍 = 𝑒  οŠͺ     ο‘½   na forma exponencial.

  • A 𝑒 β‹… 𝑒  οŠͺ  ο‘½  
  • B 𝑒 β‹… 𝑒 οŠͺ  ο‘½  
  • C 𝑒     ο‘½  
  • D 𝑒 βˆ’ 𝑒  οŠͺ  ο‘½  

Q4:

Dado que 𝑧 = √ 3 2 βˆ’ 3 2 𝑖 , encontre 𝑧  , dando sua resposta de forma exponencial.

  • A 9 √ 3 𝑒 ο‘½  
  • B √ 3 𝑒 ο‘½  
  • C 9 √ 3 𝑒 ο‘½ οŽ₯ 
  • D 5 √ 3 𝑒 ο‘½  

Q5:

Sendo 𝑧 = 1 1 ( 3 1 5 + 𝑖 3 1 5 ) c o s s e n ∘ ∘ , escreva 𝑧 na forma algΓ©brica.

  • A 𝑧 = 1 1 √ 2 2 βˆ’ 1 1 √ 2 2 𝑖
  • B 𝑧 = 1 1 √ 2 2 + 1 1 √ 2 2 𝑖
  • C 𝑧 = βˆ’ 1 1 √ 2 2 βˆ’ 1 1 √ 2 2 𝑖
  • D 𝑧 = βˆ’ 1 1 √ 2 2 + 1 1 √ 2 2 𝑖

Q6:

Sabendo que 𝑧 = 5 [ ( βˆ’ 3 3 0 ) + 𝑖 ( βˆ’ 3 3 0 ) ] c o s s e n ∘ ∘ , escreve 𝑧 na forma algΓ©brica.

  • A 𝑧 = 5 √ 3 2 + 5 2 𝑖
  • B 𝑧 = 5 √ 3 2 βˆ’ 5 2 𝑖
  • C 𝑧 = 5 2 + 5 √ 3 2 𝑖
  • D 𝑧 = βˆ’ 5 √ 3 2 βˆ’ 5 2 𝑖
  • E 𝑧 = βˆ’ 5 2 + 5 √ 3 2 𝑖

Q7:

Escreva 𝑧 = 6 ο€» βˆ’ πœ‹ 4 + 𝑖 πœ‹ 4  c o s s e n na forma exponencial.

  • A 6 𝑒  ο‘½  
  • B √ 2 2 𝑒  ο‘½  
  • C 6 𝑒 ο‘½  
  • D 𝑒 ο‘½  
  • E 𝑒  ο‘½  

Q8:

Sendo 𝑧 = 6 [ πœ‹ + 𝑖 πœ‹ ] c o s s e n , determine a forma algΓ©brica de 𝑧 .

  • A 𝑧 = βˆ’ 6
  • B 𝑧 = 6 + 6 𝑖
  • C 𝑧 = 6
  • D 𝑧 = βˆ’ 6 𝑖
  • E 𝑧 = 6 𝑖

Q9:

Sendo 𝑧 = 6 √ 2 βˆ’ 6 √ 2 𝑖 , escreva 𝑧 na forma trigonomΓ©trica.

  • A 𝑧 = 1 2  7 πœ‹ 4 + 𝑖 7 πœ‹ 4  c o s s e n
  • B 𝑧 = 3  7 πœ‹ 4 + 𝑖 7 πœ‹ 4  c o s s e n
  • C 𝑧 = 1 2  9 πœ‹ 4 + 𝑖 9 πœ‹ 4  c o s s e n
  • D 𝑧 = 1 2  7 πœ‹ 4 βˆ’ 𝑖 7 πœ‹ 4  c o s s e n
  • E 𝑧 = 1 2  1 1 πœ‹ 4 + 𝑖 1 1 πœ‹ 4  c o s s e n

Q10:

Expresse o nΓΊmero √ 3 𝑖 na forma trigonomΓ©trica.

  • A √ 3 ( 9 0 + 𝑖 9 0 ) c o s s e n ∘ ∘
  • B √ 3 ( 1 8 0 + 𝑖 1 8 0 ) c o s s e n ∘ ∘
  • C βˆ’ √ 3 ( 9 0 + 𝑖 9 0 ) c o s s e n ∘ ∘
  • D √ 3 ( 0 + 𝑖 0 ) s e n c o s ∘ ∘
  • E √ 3 ( 9 0 + 𝑖 9 0 ) s e n c o s ∘ ∘

Q11:

Expresse o nΓΊmero βˆ’ 1 + 𝑖 na forma trigonomΓ©trica.

  • A √ 2 ( 1 3 5 + 𝑖 1 3 5 ) c o s s e n ∘ ∘
  • B √ 2 ( 2 2 5 + 𝑖 2 2 5 ) c o s s e n ∘ ∘
  • C βˆ’ √ 2 ( 1 3 5 + 𝑖 1 3 5 ) c o s s e n ∘ ∘
  • D βˆ’ √ 2 ( 1 3 5 + 𝑖 1 3 5 ) s e n c o s ∘ ∘
  • E √ 2 ( 1 3 5 + 𝑖 1 3 5 ) s e n c o s ∘ ∘

Q12:

Coloque 𝑧 = 3 √ 2 ο€» βˆ’ πœ‹ 4 + 𝑖 πœ‹ 4  s e n c o s na forma exponencial.

  • A 3 √ 2 𝑒 3 πœ‹ 4 𝑖
  • B √ 2 2 𝑒 3 πœ‹ 4 𝑖
  • C 3 √ 2 𝑒 πœ‹ 4 𝑖
  • D βˆ’ 3 √ 2 𝑒 3 πœ‹ 4 𝑖
  • E 𝑒 3 πœ‹ 4 𝑖

Q13:

Qual das seguintes opçáes expressa o nΓΊmero complexo 𝑖 em coordenadas polares?

  • A ο€» 1 , πœ‹ 2 
  • B ο€» βˆ’ 1 , πœ‹ 2 
  • C ( βˆ’ 1 , πœ‹ )
  • D ( 1 , πœ‹ )

Q14:

Dado que 𝑉 = 5 √ 2 2 βˆ’ 5 √ 2 2 𝑖 , encontre a forma trigonomΓ©trica de 1 𝑉 .

  • A 1 𝑉 = 1 5  ο€Ό 7 πœ‹ 4  + 𝑖 ο€Ό 7 πœ‹ 4   c o s s e n
  • B 1 𝑉 = 1 2 5  ο€Ό 7 πœ‹ 4  + 𝑖 ο€Ό 7 πœ‹ 4   c o s s e n
  • C 1 𝑉 = 1 5  ο€Ό 9 πœ‹ 4  + 𝑖 ο€Ό 9 πœ‹ 4   c o s s e n
  • D 1 𝑉 = 5  ο€Ό 7 πœ‹ 4  + 𝑖 ο€Ό 7 πœ‹ 4   c o s s e n
  • E 1 𝑉 = 1 2 5  ο€Ό 1 1 πœ‹ 4  + 𝑖 ο€Ό 1 1 πœ‹ 4   c o s s e n

Q15:

Simplifique ( βˆ’ 1 βˆ’ 𝑖 ) 6 , dando sua resposta na forma trigonomΓ©trica.

  • A 8 ( 2 7 0 + 𝑖 2 7 0 ) c o s s e n ∘ ∘
  • B 8 ( 9 0 + 𝑖 9 0 ) c o s s e n ∘ ∘
  • C βˆ’ 8 ( 2 7 0 + 𝑖 2 7 0 ) c o s s e n ∘ ∘
  • D 8 ( 1 8 0 + 𝑖 1 8 0 ) s e n c o s ∘ ∘
  • E 8 ( 2 7 0 + 𝑖 2 7 0 ) s e n c o s ∘ ∘

Q16:

Coloque 𝑧 = βˆ’ 7 ο€» πœ‹ 4 + 𝑖 πœ‹ 4  c o s s e n na forma exponencial.

  • A 7 𝑒 5 πœ‹ 4 𝑖
  • B 7 𝑒 πœ‹ 4 𝑖
  • C βˆ’ 7 𝑒 5 πœ‹ 4 𝑖
  • D 𝑒 5 πœ‹ 4 𝑖

Q17:

Expresse o nΓΊmero complexo 𝑍 = 1 4 4 3 √ 3 + 3 𝑖 na forma trigonomΓ©trica.

  • A 𝑍 = 2 4 ο€» ο€» βˆ’ πœ‹ 6  + 𝑖 ο€» βˆ’ πœ‹ 6   c o s s e n
  • B 𝑍 = 2 4 ο€» ο€» πœ‹ 6  + 𝑖 ο€» πœ‹ 6   c o s s e n
  • C 𝑍 = 2 4 ο€» ο€» πœ‹ 6  βˆ’ 𝑖 ο€» πœ‹ 6   c o s s e n
  • D 𝑍 = 2 4 ο€» ο€» βˆ’ πœ‹ 6  βˆ’ 𝑖 ο€» βˆ’ πœ‹ 6   c o s s e n
Visualizar