Solve polynomial using complex number

[songoku]

Homework Statement

a. Solve w^3 = 1 in de moivre form

b. You must use result from (a) to solve (z + i)^3 + (z - i)^3 = 0

Relevant Equations

de moivre

I can do question (a). For question (b), I can not see the relation to question (a). Can we really do question (b) using result from (a)? Please give me little hint to relate them

Thanks

 

[member 587159]

Homework Statement: a. Solve w^3 = 1 in de moivre form

b. You must use result from (a) to solve (z + i)^3 + (z - i)^3 = 0
Homework Equations: de moivre

I can do question (a). For question (b), I can not see the relation to question (a). Can we really do question (b) using result from (a)? Please give me little hint to relate them

Thanks

Divide both sides in (b) by $(z+i)^3$ and use that $-1=(-1)^3$ to write the equation in the form

$$\left(\frac{i-z}{i+z}\right)^3=1$$

Then you can use (a) to proceed.

 

[songoku]

Divide both sides in (b) by $(z+i)^3$ and use that $-1=(-1)^3$ to write the equation in the form

$$\left(\frac{i-z}{i+z}\right)^3=1$$

Then you can use (a) to proceed.

Thank you very much