Comprehension

मान लीजिए z =  जहां i =  है

कोण θ क्या है ताकि z शुद्धतः वास्तविक है ?

जहां n एक पूर्णांक है

This question was previously asked in
NDA 02/2022 Mathematics Official Paper (Held On 04 Sep 2022)
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  1. केवल 2nπ

Answer (Detailed Solution Below)

Option 3 : nπ
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NDA 01/2025: English Subject Test
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संकल्पना:

यदि z = x + iy शुद्ध रूप से वास्तविक है, तो y = 0 है।

गणना:

दिया गया है,

z =  जहाँ i = 

(1 + i sin θ) से अंश और हर को गुणा करने पर,

चूँकि z शुद्ध रूप से वास्तविक है,

⇒ 

⇒ sin θ = 0

⇒ θ = nπ 

सही उत्तर विकल्प (3) है।

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