How do you simplify #i/(1+2i)#?

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Answer 1 · 2017-01-21T10:39:34

The answer is #=2/5+1/5i#

When you have a complex number in the denominator, multiply the numerator and denominator by the conjugate of the denominator.

#i^2=-1#

The conjugate of #(1+2i)# is #(1-2i)#

#i/(1+2i)=i/((1+2i))*((1-2i))/((1-2i))#

#=(i-2i^2)/(1-4i^2)#

#=(2+i)/5#

#=2/5+1/5i#