Question

Write the expression in standard form. five divided by quantity three minus fifteen i.

Answer 1

Standard form is a+bi where a and b are real numbers
remeber that i²=-1

ok

$\frac{5}{3-15i}$
we got to get the i out of the denomenator
remember the differnce of 2 perfect squares where (a-b)(a+b)=a²-b²

so multiply the whole thing by $\frac{3+15i}{3+15i}$
we get
$\frac{5(3+15i)}{3^2-(15i)^2}=\frac{15+75i}{9-225(-1)}=\frac{15+75i}{9+225}=$$\frac{15+75i}{234}=\frac{15}{234}+\frac{75i}{234}=\frac{15}{234}+\frac{75}{234}i=\frac{5}{78}+\frac{25}{78}i$

in standard form, it is $\frac{5}{78}+\frac{25}{78}i$