Question
Download Solution PDF\(\rm \dfrac{4+2i}{1-2i}\) का मापांक क्या है, जहाँ \(\rm i=\sqrt{-1} ?\) है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
माना कि z = x + iy एक सम्मिश्र संख्या है, जहाँ x को सम्मिश्र संख्या या Re (z) का वास्तविक भाग कहा जाता है और y को सम्मिश्र संख्या या Im (z) का काल्पनिक भाग कहा जाता है।z का मापांक = |z| = \(\rm \sqrt {x^2+y^2} = \sqrt {Re (z)^2+Im (z)^2}\)
गणना:
माना कि \(\rm z= x + iy = \dfrac{4+2i}{1-2i}\)
\(\rm = \dfrac{4+2i}{1-2i}\times\dfrac{1+2i}{1+2i}\)
\(\rm= \dfrac{4+10i+4i^2}{1-4i^2}\)
चूँकि हम जानते हैं i2 = -1
\(\rm = \dfrac{4+10i-4}{1+4}\)
\(\rm x + iy =\dfrac{10i}{5} = 0 + 2i\)
चूँकि हम जानते हैं कि यदि z = x + iy एक सम्मिश्र संख्या है, तो इसके मापांक को |z| = \(\rm \sqrt{x^2+y^2}\) द्वारा ज्ञात किया गया है।
∴ |z| = \(\rm \sqrt{0^2+2^2} = 2\)
Last updated on May 31, 2025
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