Find all of the solutions of the equation `z^(4)=81` Not sure how to work this out, would appreciate any help

1 Answer

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lemjay | High School Teacher | (Level 3) Senior Educator

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To solve, set one side equal to zero. To do so, subtract both sides by 81.



Then, factor left side.


Factor z^2-9 further.


Then, set each factor equal to zero and solve for the values of z.

For the first factor,




For the second factor,




And for the last factor,




Then, take the square root of both sides.



Since the number inside the square root is negative, the other values of z are imaginary number.


Hence, the solutions of the given equation are x = -3 , 3 , -3i and 3i.