How do you simplify #\frac { 2- 3i } { 1- 4i }#?

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Answer 1 · 2017-02-15T09:08:20

The answer is #=14/17+5/17i#

Multiply the numerator and the denominator by the conjugate of the denominator

Here, the conjugate is #=1+4i#

and #i^2=-1#

Therefore,

#(2-3i)/(1-4i)#

#=(2-3i)/(1-4i)*(1+4i)/(1+4i)#

#=(2+8i-3i-12i^2)/(1-16i^2)#

#=(2+12+5i)/(1+16)#

#=(14+5i)/(17)#

#=14/17+5/17i#