z^5=9i(z^2)

Solution for z^5=9i(z^2) equation:

Simplifying
z5 = 9i(z2)

Multiply i * z2
z5 = 9iz2

Solving
z5 = 9iz2

Solving for variable 'z'.

Reorder the terms:
-9iz2 + z5 = 9iz2 + -9iz2

Combine like terms: 9iz2 + -9iz2 = 0
-9iz2 + z5 = 0

Factor out the Greatest Common Factor (GCF), 'z2'.
z2(-9i + z3) = 0

Subproblem 1
Set the factor 'z2' equal to zero and attempt to solve:

Simplifying
z2 = 0

Solving
z2 = 0

Move all terms containing z to the left, all other terms to the right.

Simplifying
z2 = 0

Take the square root of each side:
z = {0}
Subproblem 2
Set the factor '(-9i + z3)' equal to zero and attempt to solve:

Simplifying
-9i + z3 = 0

Solving
-9i + z3 = 0

Move all terms containing z to the left, all other terms to the right.

Add '9i' to each side of the equation.
-9i + 9i + z3 = 0 + 9i

Combine like terms: -9i + 9i = 0
0 + z3 = 0 + 9i
z3 = 0 + 9i
Remove the zero:
z3 = 9i

Simplifying
z3 = 9i

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
z = {0}