Trig Question?

Question

Find all complex number solutions of x^4+16=0. Leave all answers in TRIGONOMETRIC form. 

Please show me how to do this.

Answer 1

x⁴ + 16 = 0

(x²)² + 4² = 0

Add 8x² both sides.

(x²)² + 8x² + 4² = 8x²

(x²)² + 2(x²)(4) + 4² - 8x² = 0

Apply formula : a² + 2ab + b² = ( a + b )²

( x² + 4 )² – (2√2x)² = 0

Apply formula : a² - b² = ( a + b ) ( a - b )

( x² + 4 + 2√2x) ( x² + 4 – 2√2x) = 0

( x² + 2√2x + 4 ) ( x²  – 2√2x + 4 ) = 0

By using zero product property : If AB = 0 then A = 0 and B = 0.

( x² + 2√2x + 4 ) = 0       ;         ( x²  – 2√2x + 4 ) = 0

Use formula :

Solution :

.