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$$
(1+i)^{2024}+(1-i)^{2024}=
$$
Options:
(1+i)^{2024}+(1-i)^{2024}=
$$
Solution:
1516 Upvotes
Verified Answer
The correct answer is:
$2^{1013}$
$\begin{aligned} & \text { }(1+i)^{2024}+(1+i)^{2024}=\left[(1+i)^2\right]^{1012}+\left[(1-i)^2\right]^{1012} \\ & =\left[(2 i)^{1012}\right]+[(-2 i)]^{1012} \\ & =(2)^{1012}(i)^{1012}+(-2)^{1012}(i)^{1012} \\ & =2 \cdot 2^{1012}=2^{1013}\end{aligned}$
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