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If Z = 1 − Cos θ + I Sin θ , Then | Z | = - Mathematics

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प्रश्न

\[\text { If  }z = 1 - \text { cos }\theta + i \text { sin }\theta, \text { then } \left| z \right| =\]

पर्याय

  • \[2 \sin\frac{\theta}{2}\]

  • \[2 \cos\frac{\theta}{2}\]

  • \[2\left| \sin\frac{\theta}{2} \right|\]

  • \[2\left| \cos\frac{\theta}{2} \right|\]

MCQ
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उत्तर

\[2\left| \sin\frac{\theta}{2} \right|\]

\[\because z = 1 - \cos\theta + i \sin\theta\]

\[ \Rightarrow \left| z \right| = \sqrt{\left( 1 - \cos\theta \right)^2 + \sin^2 \theta}\]

\[ \Rightarrow \left| z \right| = \sqrt{1 + \cos^2 \theta - 2\cos\theta + \sin^2 \theta}\]

\[ \Rightarrow \left| z \right| = \sqrt{1 + 1 - 2\cos\theta}\]

\[ \Rightarrow \left| z \right| = \sqrt{2\left( 1 - \cos\theta \right)}\]

\[ \Rightarrow \left| z \right| = \sqrt{4 \sin^2 \frac{\theta}{2}}\]

\[ \Rightarrow \left| z \right|=2\left| \sin\frac{\theta}{2} \right|\]

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पाठ 13: Complex Numbers - Exercise 13.6 [पृष्ठ ६५]

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आरडी शर्मा Mathematics [English] Class 11
पाठ 13 Complex Numbers
Exercise 13.6 | Q 23 | पृष्ठ ६५

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