Question

Write the expression in standard form.

5/(3-15i)

Answer 1

multiply the numerator and denominator by the denominator's conjugate
$$
\cfrac{5}{3-5i} \times \cfrac{3+5i}{3+5i}
$$

Answer 2

keep in mind the difference of squares, \((a-b)(a+b) = (a^2-b^2)\)

Answer 3

is the answer \[\frac{ 5 }{ 78} + \frac{ 25 }{ 78 }i\]

Answer 4

yes?

Answer 5

so is this the right answer?

Answer 6

well
$$
\cfrac{5}{3-5i} \times \cfrac{3+5i}{3+5i}\\
\implies \frac{5(3+5i)}{3^2-(5i)^2}
\implies \frac{15+25i}{9-25(i^2)}
$$

Answer 7

wait, you have 15i, lemme rewrite that using 15i, NOT 5i

Answer 8

$$ \large {
\cfrac{5}{3-15i} \times \cfrac{3+15i}{3+15i}\\
\implies \frac{5(3+15i)}{3^2-(15i)^2}
\implies \frac{15+75i}{9-225(i^2)}
}
$$

Answer 9

yes after this is where i got lost

Answer 10

now, \(i^2 = (\sqrt{-1})^2 \implies -1\)

Answer 11

i^2 is -1 so it would be \[\frac{ 15+75i }{ 9+225 }\]

Answer 12

right

Answer 13

\[\frac{ 15+75i }{ ?234}\]

Answer 14

yes, can further simplify it by getting common factor of "3" above and below

Answer 15

ok thank you

Answer 16

$$ \large{
\cfrac{ \cancel{3}(5+25i) }{ \cancel{3}(78) }
}
$$

Answer 17

yw

Answer 18

or 5/78 + (25/78)i