Ola Matheus

z = (1 - i)/(1 + √3i) = (1 - i)*(1 - √3i)/(1 - √3i)*(1 + √3i)

z = (1 - √3i - i - √3)/(1 + 3) = (1-√3)/4 - i*(1+√3)/4

a = (1 - √3)/4

b = -(1 + √3)/4

argumento

¦z¦ = √(a² + b²)

¦z¦ = √((1 - √3)²/16 + (1 - √3)²/16)

¦z¦ = √(1 - 2√3 + 3 + 1 - 2√3 + 3)/16

¦z¦ = √8/16 = √2/2

a = (1 - √3)/4

b =- (1 + √3)/4

z = √2/2 *( (1 - √3)*2/4√2 + i(-1 - √3)*2 )/4√2

z = √2/2 *( (√2 - √6)/4 + i(√2 + √6)/4

z = √2/2 * (cos(-105°) + i*sen(-105°))

pronto