How do you simplify #i/(7+4i) #?

1 Answer
mason m
Mar 6, 2016

#4/65+7/65i#

Explanation:

In order to remove the complex number from the denominator, we need to multiply the fraction by the complex conjugate.

#=i/(7+4i)((7-4i)/(7-4i))#

Distribute.

#=(7i-4i^2)/(49+28i-28i-16i^2)#

We can simplify this knowing that since #i=sqrt(-1)=>ul(i^2=-1)#.

#=(7i-4(-1))/(49-16(-1))#

#=(4+7i)/(49+16)#

#=(4+7i)/65#

#=4/65+7/65i#

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