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Complex Numbers — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers1 Mark
Question
Simplify
$\frac{ i ^{29}+ i ^{39}+ i ^{49}}{ i ^{30}+ i ^{40}+ i ^{50}}$
✓

Answer

$\frac{i^{29}+i^{39}+i^{49}}{i^{30}+i^{49}+i^{30}}$
$=\frac{i^{29}+i^{39}+i^{49}}{i\left(i^{29}+i^{39}+i^{49}\right)}=\frac{1}{i}=\frac{i}{i^2}=\frac{i}{-1}$
$=- i$

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