Let z1 = 4 ( cos (7𝜋/ 12) + i sin (7𝜋/ 12)) and z2 = 2 (cos (5𝜋 /12) + i sin (5𝜋 /12)) . Find z1z2 and z1 z2 . (Enter your answers in a + bi form.)

Question

Let z1 = 4 ( cos (7𝜋/ 12) + i sin (7𝜋/ 12)) and z2 = 2 (cos (5𝜋 /12) + i sin (5𝜋 /12)) . Find z1z2 and z1 z2 . (Enter your answers in a + bi form.) z1z2=_____, z1/z2=_____

Answer 1

z₁z₂ = 8[cos(7π/12 + 5π/12) + isin(7π/12 + 5π/12)] = 8(cosπ + isinπ) = - 8

z₁/z₂ = 4/2[cos(7π/12 - 5π/12) + isin(7π/12 - 5π/12)] = 2(cosπ/6 + isinπ/) = √3 + i