Solve each equation. Then graph the root in the complex plane
x^5+1=0 This is what I did
So that means -1+0i r= square root 1+0 so r=1 theta would be 0/1 or o
So would the polar form be 1(cos o+ i sin 0)? Did I set this problem up right?
This is the formula from my textbook I am encouraged to apply
(a+bi)^(1/p)= r^1/p cos theta+2(n)pi/p+ i sin theta+ 2(n)pi/p
I have a new question I need to clarity now that I have solved the question I asked earlier.
It involved solving this equation 3x^4+48=0 This is what I did
So in that case -12+0i I got r=12 and theta equals=pi
Then I plugged in 12^(1/4) (cos pi+2pi(0)/4) + i sin (pi+2pi(0)/4)
I end up getting 1.861 (.707+.707)
1.315+1.315i But I think my answer is wrong.
See I know cos (180/4)=.707
For starters, -48 divided by 3 is NOT -12. Also, you will be expected to use exact values of the correct value of x. Furthermore, you are expected to use the exact surd value of cos(180/4 degrees) = cos(45 degrees) and sin(45 degrees) and get exact surd values for the cartesian form of the solutions (if cartesian form is required).
Sorry, but what I have said is a harsh reality - life is not going to get easier by ignoring the problem.