Question
Download Solution PDFयदि x = (cos π/14 + i sin π/14), y = (cos 9π/14 + i sin 9π/14) है, तो x5 ⋅ y15 का मान ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
\({e^{i\; ⋅ \;\theta }} = \cos \theta + i\sin \theta \)
गणना:
दिया गया है:
x = (cos π/14 + i sin π/14), y = (cos 9π/14 + i sin 9π/14)
चूँकि हम जानते हैं कि,
\({e^{i\; ⋅ \;\theta }} = \cos \theta + i\sin \theta \)
हम x और y को निम्न रूप में लिख सकते हैं:
⇒ x = ei ⋅ π/14 और y = ei ⋅ 9π/14
⇒ x5 = ei ⋅ 5π/14 और y15 = ei ⋅ 135π/14
⇒ x5 ⋅ y15 = ei ⋅ 10π
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