How can i write (1+2i)(3+i) divide by -2+i in the form a+bi?

1 Answer
Feb 18, 2018

#1-3i#

Explanation:

#•color(white)(x)i^2=(sqrt(-1))^2=-1#

#"first expand the factors "(1+2i)(3+i)#

#=3+i+6i+2i^2=1+7i#

#rArr(1+7i)/(-2+i)#

#"to "color(blue)"rationalise"" the denominator"#

#"multiply numerator/denominator by the "color(blue)"complex conjugate"" of the denominator"#

#"the conjugate of "-2+i" is "-2color(red)(-)i#

#rArr((1+7i)(-2-i))/((-2+i)(-2-i))#

#"expand factors on numerator/denominator"#

#=(-2-15i-7i^2)/(4-i^2)#

#=(5-15i)/5=1-3ilarrcolor(red)"in standard form"#