How do you simplify #(2+5i)/(5+4i)#?

Question

Treat #i# as an imaginary number,

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Answer 1 · 2016-11-26T06:30:24

The answer is #=30/41+(17i)/41#

If you want to simplify a quotient of complex numbers , multiply numerator and denominator by the conjugate of the denominator.

#z=z_1/z_2=(z_1barz_2)/(z_2barz_2)#

The conjugate of #(a+ib)# is #(a-ib)#

And #i^2=-1#

Here, #z_1=2+5i# and #z_2=5+4i#

So #(2+5i)/(5+4i)=((2+5i)(5-4i))/((5+4i)(5-4i))#

#=(10-8i+25i-20i^2)/(25-16i^2)#

#=(30+17i)/(41)#

#=30/41+(17i)/41#