Z^5=-7776i

Find the solution of the following equation whose argument is strictly between 270 and 360 degrees

Z=+6

Step-by-step explanation:

Z^5=-7776i

Let's note that i I mathematics means negative one i. e

i = - 1

So the equation is equal to

Z^5=- * - (7776)

Z^5 = 7776

Z = 5√7776

Since it's a divisible by 6

It's giving us a clue that 6 it's the answer.

Ok let's check the 5th root of 7776 in our calculator.

Z=+6

+6 is the solution to the equation

Z^5=-7776i