Solve the equation. (Enter your answers as a comma-separated list. Do not use cis form.)x4 + 81 = 0
Question
Solve the equation.
(Enter your answers as a comma-separated list. Do not use cis form.)
Solution
The given equation is x^4 + 81 = 0.
Step 1: We can rewrite the equation as x^4 = -81.
Step 2: Taking the fourth root on both sides, we get x = ±√4√(-81).
Step 3: We know that √(-1) = i (imaginary unit), so we can rewrite the equation as x = ±√4√(-1*81) = ±√4√(81)i.
Step 4: Simplifying further, we get x = ±2√81i = ±2*9i = ±18i.
So, the solutions to the equation are x = 18i and x = -18i.
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