How do you divide #( 1+6i)/(4+2i)#?

1 Answer
sente
Jan 29, 2016

#(1+6i)/(4+2i)=4/5+11/10i#

Explanation:

The conjugate of a complex number #a+bi# is #a-bi#. Using the fact that the product of a complex number and its conjugate is a real number, we can simply the given expression by multiplying the numerator and denominator by the conjugate of the denominator.

#(1+6i)/(4+2i) = ((1+6i)(4-2i))/((4+2i)(4-2i))#

#=(4+24i-2i+12)/(16+8i-8i+4)#

#=(16+22i)/20#

#=4/5+11/10i#

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