Question

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ASSOCIE AS COORDENADAS POLARES RELACIONADAS NA COLUNA DA ESQUERDA CO AS SUAS RESPECTIVAS COORDENADAS CARTESIANAS RELACIONADAS NA COLUNA DA DIREITA:

Answer 1

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I)  P(2, π/3) 

z = 2*(cos(π/3) + isen(π/3))
z = 2*(1/2 + i√3/2 = 1 + √3i  ⇒ P(1,√3) (3)

II) P(5, -π/4)

z = 5*(cos(-π/4) + isen(-π/4))
z = 5*(√2/2, -√2/2) = 5√2/2 - 5√2i/2 ⇒ P(2.5√2 - 2.5√2) (6)

III) P(3, -π/2)

z = 3*(cos(-π/2) + isen(-π/2))
z = 3*(0 - i) = (0, 3i) ⇒ P(0, -3) (4)

IV) P(2,π/6) 

z = 2*(cos(π/6) + isen(π/6)) 
z = 2*(√3/2, i/2) = 2√3/2 + 2i/2 = √3 + i ⇒ P(√3,1) (1)

V) P(3, -π/3)

z = 3*(cos(-π/3) + isen(-π/3))
z = 3*(1/2 - i√3/2) = 1.5 - 1.5√3i ⇒ P( 1.5 ,- 1.5√3) (5)

VI) P(5, π/4)

z = 5*(cos(π/4) + isen(π/4))
z = 5*(√2/2 + i√2/2) = 2.5√2 + 2.5√2i ⇒ P(2.5√2, 2.5√2) (2)