Question
Download Solution PDFi500 + i501 + i502 का मान, जहां \({\rm{i}} = \sqrt { - 1} \) _____ है।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा:
i की घात:
- i = \(\sqrt{-1}\)
- i2 = -1
- i3 = i × i2 = -i
- i4 = (i2)2 = (-1)2 = 1
- i4n = 1
गणना:
खोजने के लिए: i500 + i501 + i502 का मान
जैसा कि हम जानते हैं i2 = -1
i500 + i501 + i502
= i500 [1 + i + i2]
\(\rm =\left ( i^{4} \right )^{125}(1+i+i^{2})\)
= 1 + i + i2
= 1 + i - 1
= i
∴ i500 + i501 + i502 = i
इसलिए, विकल्प 1 सही है
Last updated on May 31, 2025
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