Solve using complex number system

Question

x^3+64=0 Solve by completing the square

Answer 1

x³ + 64 = 0

 

(x + 4)(x² - 4x + 16) = 0

 

Real root: x = 4

 

Complex roots:

 

x² - 4x + 16 = 0

 

x² - 4x + 4 = -12

 

(x - 2)² = -2²·3

 

x - 2 = ±2√3 i

 

x = 2 ± 2√3 i

Answer 2

x³ + 64 = 0

 

x³ = -64

 

x = -4

 

 

Since we want to use complex numbers, we use the fact that     i² = -1 ,

 

x = 4  * -1

 

x = 4 * i²

 

Answer 3

X^3 = - 64

 

X = cube root - 64 

 

= -4

 

= 4 × -1

 

= 4 i