How do you divide # (6-i) / (1-i) #?

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Answer 1 · 2016-01-19T05:30:17

Explanation is given below.

For dividing complex numbers, you just need to multiply the numerator and denominator by the conjugate of the denominator.

If the complex number is #a+ib# then the conjugate is given by #a-ib#. #color(red) "The imaginary term sign has to be changed"#

In our problem #(6-i)/(1-i)#

The denominator is #(1-i)# remember for the conjugate we change the sign of the denominator.

The conjugate of #1-i# is #1+i#

So we have

#(6-i)/(1-i)xx(1+i)/(1+i)#

#=((6-i)(1+i))/((1-i)(1+i))#

#=(6-6i-i+i^2)/(1^2-i^2)#

#=(6-7i-1)/(1-(-1))#

#=(7-7i)/(1+1)#

#=(7-7i)/2#

#=7/2 - 7/2i#