How do you simplify #(2-3i) div (1+5i)#?

1 Answer
George C.
Jan 2, 2016

Multiply dividend and divisor by the Complex conjugate of the divisor then simplify to find:

#(2-3i)-:(1+5i) = -1/2 - 1/2i#

Explanation:

The Complex conjugate of the divisor is #(1-5i)#.

If we multiply both the dividend and the divisor by #(1-5i)# and simplify then we will get a Real divisor without altering the quotient...

#(2-3i)/(1+5i)#

#=((2-3i)(1-5i))/((1+5i)(1-5i))#

#=(2-10i-3i+15i^2)/(1^2-color(red)(cancel(color(black)(5i)))+color(red)(cancel(color(black)(5i)))-(5i)^2)#

#=(-13-13i)/(1+25)#

#=(-13(1+i))/26#

#=-1/2-1/2i#

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