Last updated at Dec. 8, 2016 by Teachoo

Transcript

Misc 15 Find the modulus of (1 + ๐)/(1 โ ๐) โ (1 โ ๐)/(1 + ๐) First we solve (1 + ๐)/(1 โ ๐) โ (1 โ ๐)/(1 + ๐) (1 + ๐)/(1 โ ๐) โ (1 โ ๐)/(1 + ๐) = ((1 + ๐) ร (1 + ๐) โ(1 โ ๐) ร (1 โ ๐))/((1โ๐) (1+ ๐)) = ((1 + ๐)2 โ ( 1 โ ๐ )2)/((1 โ ๐) (1 + ๐)) Using a2 โ b2 = (a + b) (a โ b) = ([( 1+ ๐ ) + ( 1 โ ๐ )] [( 1+ ๐ ) โ ( 1 โ ๐ )])/((1)2 โ(๐)2) = (( 1 + 1 + ๐ โ ๐ ) ( ๐ + ๐ + 1 โ1 ))/( 1 โ ๐2) = (( 2 + 0 ) ( 2๐ + 0 ))/(1 โ ๐2) = ((2) (2๐))/(1 โ๐2) = 4๐/(1 โ๐2) Putting i2 = - 1 = 4๐/( 1โ ( โ 1 ) ) = 4๐/( 1 + 1) = ( 4๐)/( 2) = 2๐ = 0 + 2๐ Thus , (1 + ๐)/(1 โ ๐) โ (1 โ ๐)/(1 + ๐) = 0 + 2๐ Thus , (1 + ๐)/(1 โ ๐) โ (1 โ ๐)/(1 + ๐) = 0 + 2๐ We need to find modulus of (1 + ๐)/(1 โ ๐) โ (1 โ ๐)/(1 + ๐) Complex number (0 + 2๐) is of the form x + ๐y Hence x = 0 and y = 2 Modulus of z = |z| |z| = โ(๐ฅ^2+๐ฆ2) = โ((0)2+(2)2) = โ(0+4) = โ4 = 2 Hence, Modulus of (1 + ๐)/(1 โ ๐) โ (1 โ ๐)/(1 + ๐) = 2

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.