Solve in complex number system: x^4 + x^2 - 4 = 0

[sisterofmaddie]

Solve in complex number system: x^4 + x^2 - 4 = 0

I think you need to factor this and solve for x^2. I'm just not sure how to get there! I know that there will be imaginary/complex numbers involved as well.

 

[arthur ohlsten]

You are correct
To have the equation look more familiar let us set z=x^2

x^4+x^2-4=0
z^2+z-4=0 quadratic equation

z=-1+/-[1+16]^1/2 all over 2
z=-1+/-[17]^1/2 all over 2
z= [-1+[17]^1/2]/2 z=[-1-[17]^1/2]/2
for ease I will change to decimal numbers
z=1.5616 z=-2.56

but z=x^2
x^2=1.5616 x^2=-2.5616
x=+/- 1.25 x=+/- i1.6

x=1.25 answer
x=-1.25 answer
x=1.6 i answer
x=-1.6 i answer

two real and two "imaginary" or complex answers

Arthur