1. Complex numbers

hi all,

i need help with two problems that read: "solve the equation in the complex number system."

&

hi all,

i need help with two problems that read: "solve the equation in the complex number system."

&

$x^4 = 256$

$(x^2)^2 = 256$

$x^2 = \pm 16$.

Case 1: $x^2 = 16$

$x = \pm 4$.

Case 2: $x^2 = -16$

$x = \pm 4i$.

So the four solutions are $4, 4i, -4, -4i$.

3. The second expression, $x^3- 343$, isn't and equation but I assume you meant $x^3= 343$. Since the first equation had a simple integer solution, x= 2, the first thing you should do is start cubing integers. You find that $7^3= 343$. Then $x^3- 7^3= (x- 7)(x^2+ 7x+ 49)$. x= 7 is one solution and you can find the other two by solving $x^2+7x+ 49= 0$ with the quadratic formula.