Question

Write the expression in standard form.
six divided by quantity four minus thirteen i.

Answer 1

\[\frac{6}{4-13i}\]?

Answer 2

yes c:

Answer 3

multiply top and bottom by the conjugate of the denominator
the conjugate of \(a+bi\) is \(a-bi\) and this works because \((a+bi)(a-bi)=a^2+b^2\) a real number

Answer 4

in your case you have \(4-13i\) and the conjugate is \(4+13i\)
start with
\[\frac{6}{4-13i}\times \frac{4+13i}{4+13i}=\frac{6(4+13i)}{4^2+13^2}\]

Answer 5

you probably want to multiply out in the top and compute the bottom also

Answer 6

24+78i?

Answer 7

that is the numerator
also compute the denominator, then break apart to write in standard form

Answer 8

i get \(185\) for \(4^2+13^2\) so it is
\[\frac{24+78i}{185}\] standard form is \(a+bi\) so final answer is
\[\frac{24}{185}+\frac{78}{185}i\]