Fourth roots of 81(cos320°+isin320°)

Using the De Moivre's Theorem, let us work out for the fourth roots of 81(cos 320° + i sin 320° ).

zⁿ = rⁿ (cos nθ + i sin nθ) 

z⁴ = 81(cos 320° + i sin 320° ) 

z = ∜[81(cos 320° + i sin 320° )] 

= ∜[3^4 (cos 4*80° + i sin 4*80°)] 

= 3(cos 80° + i sin 80°) 

a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. because no real number satisfies this equation, i is called an imaginary number. has no real solution, since the square of a real number cannot be negative.