Question

Determine o argumento principal dos números complexos a seguir... favor me ajudem com as letras B , C e D..

Answer 1

a)

Z1= 4 + 4i

Z1 = a + b.i

a = 4; b = 4

z = √(4^2) + (4^2)

z = √32

Z = √16.√2

Z = 4√2

Sen @ = b/z

Sen @ = 4/4√2

Sen @ = 1/√2 . √2/√2

Sen @ = √2/2

Cos @ = a/z

Cos @ = 4/4√2

Cos @ = 1/√2

Cos @ = √2/2

45° ou π/4

B)

Z2 = - √3 + i

Z2 = a + b.i

A = -√3; b = 1

Z = √(-√3)^2 + 1^2

Z = √(3+1)

Z = √4

Z = 2

Sen @ = b/z

Sen @ = 1/2

Cos @ = a/z

Cos @ = - √3/2

@ = 150° ou 5π/6

C)

Z4 = 2 - i.2√3

a = 2; b = - 2√3

Z = √(2)^2 + (-2√3)^2

Z = √(4 + (4.3)

Z = √(4+12)

Z = √16

Z = 4

Sen @ = b/z

Sen @ = -2√3/4

Sen @ = - √3/2

Cos @ = a/z

Cos @ = 2/4 = 1/2

@ = 300 ou 5π/3

D)

Z5 = -9

a = - 9; b = 0

Z = √(-9)^2 + 0^2

Z = √81

z = 9

Sen@= b/z

Sen @ = 0/9= 0

Cos@ = a/z

Cos@= -9/9= - 1

@ = 180° ou π