Question

Simplify the following quotient of complex numbers into the form a + bi.

1+8i
-------
-6+i

Answer 1

multiply numerator and denominator by the conjugate of the denominator. the conjugate of
\[a+bi\] is
\[a-bi\] and
\[(a+bi)(a-bi)=a^2+b^2\] so you will get a real number in the denominator

Answer 2

in this case you get
\[\frac{(1+8i)(-6-i)}{6^2+1^2}=\frac{(1+8i)(-6-i)}{37}\]

Answer 3

so your actual job it to multiply out in the numerator. is it clear how to do that?

Answer 4

in think so

Answer 5

yeah i get it

Answer 6

then don't forget to split the number up so it is in standard form

Answer 7

ok

Answer 8

and let me know when you get
\[\frac{2}{37}-\frac{49}{37}i\]

Answer 9

i think its 47/37