 #1
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 1
 Homework Statement:

Why does the TI83+ calculator think ## (\sqrt[4] {1})^4 = 1 + 2\times 10^{13}i ##?
(Calculator is in mode a+bi and degrees. )
 Relevant Equations:
 ##(\sqrt[4] {1})^4##
I think the solution should be:
METHOD #1:
\begin{align} (\sqrt[4] {1})^4 & = (1)^{\frac 4 4} \nonumber \\ & = (1)^1 \text{, can reduce 4/4 since base is a constant and not a variable in ℝ} \nonumber \\ & = 1 \nonumber \end{align}
Alternatively, METHOD #2 for same answer is:
\begin{align} (\sqrt[4] {1})^4 & = ((1)^{\frac 1 4})^4 \nonumber \\ & = \left\{\left[(1)^{\frac 1 2}\right]^{\frac 1 2}\right\}^4 \nonumber \\ & = (\sqrt[] {i})^4 \nonumber \\ &= i^{\frac 4 2} \nonumber \\ &= i^2 \nonumber \\ &= 1 \nonumber \end{align}
However, TI83+ calculator thinks that the solution is:
METHOD #1:
\begin{align} (\sqrt[4] {1})^4 & = (1)^{\frac 4 4} \nonumber \\ & = (1)^1 \text{, can reduce 4/4 since base is a constant and not a variable in ℝ} \nonumber \\ & = 1 \nonumber \end{align}
Alternatively, METHOD #2 for same answer is:
\begin{align} (\sqrt[4] {1})^4 & = ((1)^{\frac 1 4})^4 \nonumber \\ & = \left\{\left[(1)^{\frac 1 2}\right]^{\frac 1 2}\right\}^4 \nonumber \\ & = (\sqrt[] {i})^4 \nonumber \\ &= i^{\frac 4 2} \nonumber \\ &= i^2 \nonumber \\ &= 1 \nonumber \end{align}
However, TI83+ calculator thinks that the solution is:
## (\sqrt[4] {1})^4 = 1 + 2\times 10^{13}i ##
The calculator on https://www.symbolab.com/ gets the answer 1 which is the same as what I calculated. So, why is the TI83+ calculator getting a different answer? (And I'm assuming that my answer is correct?
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