Z^5=-243i, find the solution to the equation whose argument is strictly between 180 degrees and 270 degrees. Round your answer to the nearest 10th

The solution is .

Step-by-step explanation:

Complex power is determined by means of the De Moivre's Theorem, whose expression is:

Where is the norm of the complex number. In this case, expression can be written as:

The real component must be equal to zero and complex component must be equal to -1. That is to say:

Possible solutions for each component are, respectively:

Real component

,

,

Possible solutions: , ,

Complex component

,

,

Possible solutions: ,

There is one solution whose argument is strictly between 180 degrees () and 270 degrees ().