ƶ₁ • ƶ₂ = (4 + 4i√3) • (-4√3 + 4i)

   ƶ₁ • ƶ₂ = -16√3 + 16i – 48i + 16i²√3

   ƶ₁ • ƶ₂ = -16√3 + 16i – 48i – 16√3

   ƶ₁ • ƶ₂ = -32√3 – 32i  ◀◀

   ∠ (ƶ₁ • ƶ₂)   =   tan ‾ ¹  [-32 ⁄ (-32√3)]   =   210º  (3rd quadrant)  ◀◀

(4 + 4i√3) (-4√3 + 4i)

Foil

-16√3 + 16i - 16i*3 + 16i²√3

-16√3 + 16i - 48i - 16√3

Combine like terms

-32√3 - 32i <–––––

-----------------

tanø = -32 / -32√3

Both negative so ø is in Quad III

tanø = 1/√3

Arctan 1/√3 = 30º

In Quad III

ø = 180º + 30º

ø = 210º <–––––

http://goo.gl/y49sTR

ok