Answer:
Step-by-step explanation:
The given system of equations is now reduced:
1) 
, 
, 
, 
Given
2) 
By 1)
3) 
2) in 1)
4) 
By 1)
5) ![[c+(b+c)]+b = c](https://tex.z-dn.net/?f=%5Bc%2B%28b%2Bc%29%5D%2Bb%20%3D%20c)
4) in 3)
6) 
Algebra
7) 
Algebra
8) 
7) in 4)/Algebra
9) 
7) and 8) in 2)/Algebra
10) 9), 1), 7) and 8)/Algebra/Result
<span>use De Moivre's Theorem:
⁵√[243(cos 260° + i sin 260°)] = [243(cos 260° + i sin 260°)]^(1/5)
= 243^(1/5) (cos (260 / 5)° + i sin (260 / 5)°)
= 3 (cos 52° + i sin 52°)
z1 = 3 (cos 52° + i sin 52°) ←← so that's the first root
there are 5 roots so the angle between each root is 360/5 = 72°
then the other four roots are:
z2 = 3 (cos (52 + 72)° + i sin (52+ 72)°) = 3 (cos 124° + i sin 124°)
z3 = 3 (cos (124 + 72)° + i sin (124 + 72)°) = 3 (cos 196° + i sin 196°)
z4 = 3 (cos (196 + 72)² + i sin (196 + 72)°) = 3 (cos 268° + i sin 268°)
z5 = 3 (cos (268 + 72)° + i sin (268 + 72)°) = 3 (cos 340° + i sin 340°) </span>
This should not be in the elementary school section I didn't even learn about this....
