Question #e2b10

1 Answer
Somebody N.
Oct 20, 2017

#color(blue)(1+3i)#

Explanation:

We first need to make the denominator a real number. we can do this by multiplying top and bottom by the conjugate of #(2-i)#, this is #(2+i)#. The product of a complex number and its conjugate is always a real number. So:

#((2+i)(5+5i))/((2+i)(2-i))=( (10+10i+5i+5i^2))/(4+2i-2i-i^2)#

#-> =( (10+15i+5(-1)))/(4-(-1))= (5+15i)/5=color(blue)(1+3i)#

#color(red)((i=sqrt(-1)=> i^2=-1))#

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