Write the fraction-3+4i/-1+3i?

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1 Answer
Jim G.
Mar 12, 2018

#3/2+1/2i#

Explanation:

#•color(white)(x)i^2=(sqrt(-1))^2=-1#

#•color(white)(x)(a-b)(a+b)=a^2-b^2#

#•color(white)(x)sqrtaxxsqrta=a#

#"multiply numerator/denominator by the "color(blue)"conjugate"#
#"of the denominator"#
#"this ensures the denominator is rational"#

#"the "color(blue)"conjugate ""of"-1+3i" is "-1color(red)(-)3i#

#rArr(-3+4i)/(-1+3i)xx(-1-3i)/(-1-3i)#

#=((-3+4i)(-1-3i))/((-1+3i)(-1-3i))larrcolor(blue)"expand factors"#

#=(3-4i+9i-12i^2)/(1-9i^2)#

#=(15+5i)/10=3/2+1/2i#

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