Question
Download Solution PDFz = (1 - i)4 का मापांक ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा :
- i2 = - 1
- यदि z = x + iy तब \(|z| = \sqrt{x^2 + y^2}\)
गणना :
दिया गया: z = (1 - i)4
पहले अभिव्यक्ति (1 - i)4 को सरल करें
⇒ (1 - i)2 = 1 + i2 - 2i
जैसा कि हम जानते हैं कि, i2 = - 1
⇒ (1 + i)2 = -2i
Since (1 - i)4 = (1 - i)2 × (1 - i)2 we get:
⇒ (1 + i)4 = (-2i)2 = - 4
⇒ z = - 4 + 0i
जैसा कि हम जानते हैं कि, यदि z = x + iy तो \(|z| = \sqrt{x^2 + y^2}\)
यहाँ, x = - 4 और y = 0
⇒ \(|z| = \sqrt{(-4)^2 + 0^2} = \pm 4\)
जैसा कि हम जानते हैं कि |z| आरगां समतल में मूल और z के बीच की दूरी को दर्शाता है। तो, |z| ऋणात्मक नहीं हो सकता
⇒ |z| = 4
इसलिए, सही विकल्प 2 है।
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