Gujarat BoardEnglish MediumSTD 11 ScienceMATHSComplex Numbers3 Marks
Question
Show that $1+\text{i}^{10}+\text{i}^{20}+\text{i}^{30}$ is a real number.
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Answer
$1+\text{i}^{10}+\text{i}^{20}+\text{i}^{30}=1+\text{i}^{4\times2}\times\text{i}^2+\text{i}^{4\times5}+\text{i}^{4\times7}\times\text{i}^2$ $=1+1\times\text{i}^2+1+1\times\text{i}^2$ $=1-1+1-1$$=0,$ which is real number.
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