How do you simplify 9/(7+i)97+i?

1 Answer
Lucio Falabella
Jan 13, 2016

9/(7+i)=(63-9i)/(50)=63/50-9/50i97+i=63−9i50=6350−950i

Explanation:

  1. Find the complex coniugate of denominator

denominator: z=7+iz=7+i

denominator complex coniugate: bar(z)=7color(red)-i¯z=7−i

  1. Multiply both numerator and denominator for the complex coniugate

(9)/(7+i)*(7-i)/(7-i)=(63-9i)/(7^2-(i)^2)=97+i⋅7−i7−i=63−9i72−(i)2=

Remembering that: i^2=-1i2=−1

=(63-9i)/(49-(-1))=(63-9i)/(49+1)=(63-9i)/(50)=63/50-9/50i=63−9i49−(−1)=63−9i49+1=63−9i50=6350−950i

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