SOLUTION: Solve each equation in the complex number system. 1. x^4 = 16 2. x^4 + 13x^2 + 36 = 0

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Solve each equation in the complex number system. 1. x^4 = 16 2. x^4 + 13x^2 + 36 = 0      Log On


   

Question 1207603: Solve each equation in the complex number system.

1. x^4 = 16

2. x^4 + 13x^2 + 36 = 0
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

1.
x%5E4+=+16
x%5E4+=+2%5E4
=>+x=2+or x=-2

2.
x%5E4+%2B+13x%5E2+%2B+36+=+0
x%5E4+%2B+4x%5E2%2B+9x%5E2+%2B+36+=+0
%28x%5E4+%2B+4x%5E2%29%2B+%289x%5E2+%2B+36%29+=+0
x%5E2%28x%5E2+%2B+4%29%2B9+%28x%5E2+%2B+4%29+=+0
%28x%5E2+%2B+4%29+%28x%5E2+%2B+9%29+=+0

solutions:
x%5E2+%2B+4+=+0+
x%5E2+=-+4
x=sqrt%28-4%29
x=2i or+x=-2i
and
x%5E2+%2B+9+=+0
x%5E2+=-+9
x=sqrt%28-9%29
x=3i or x=-3i

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Both equations are polynomials of degree 4; each has 4 solutions. For the first problem, the other tutor found two solutions "by inspection", which does not provide a complete solution.

1. x^4=16

For all polynomial equations of degree greater than 1, write the equation with "0" on one side and solve by factoring if possible.

x%5E4-16=0
%28x%5E2%2B4%29%28x%5E2-4%29=0
%28x%2B2i%29%28x-2i%29%28x%2B2%29%28x-2%29=0

Solutions: 2, -2, 2i, -2i

2. x^4+13x^2+36=0

x%5E4%2B13x%5E2%2B36=0
x%5E2%2B9%29%28x%5E2%2B4%29=0
%28x%2B3i%29%28x-3i%29%28x%2B2i%29%28x-2i%29=0

Solutions: 2i, -2i, 3i, -3i