How do you divide #(-7+6i)/(7-10i)#?

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Answer 1 · 2016-12-01T08:29:48

#-109/149-28/149i#

You can multiply both the terms of the fraction by the same expression #7+10i# to get:

#((-7+6i)(7+10i))/((7-10i)(7+10i))#

#=(-49-70i+42i+60i^2)/(49-100i^2)#

Then, since #i^2=-1#, you get

#=(-49-28i-60)/(49+100)#

#=(-28i-109)/149#

that's, in standard form:

#=-109/149-28/149i#