Question

Write the expression in standard form.
3/(3-12i)

Answer 1

what would be the conjugate of the denominator?

Answer 2

3+12i

Answer 3

yes, so let's use that, to multiply the rational by 1, a/b * 1 = a/b, so is fine, so let's do that :)

Answer 4

$$\bf \color{blue}{\cfrac{3+12i}{3+12i} =1}\\
\cfrac{3}{3-12i} \times \cfrac{3+12i}{3+12i}\\
\cfrac{3(3+12i)}{(3-12i)(3+12i)}\\
\text{keep in mind that}\\
(a-b)(a+b) = (a^2-b^2)\\
$$

so what would that give you in the denominator?

Answer 5

9-(12i^2) which is 9+144

Answer 6

yes

Answer 7

so that would give you \(\bf \cfrac{9+36i}{153} \implies \cfrac{9}{153}+\cfrac{36i}{153}\)

Answer 8

so that would be the so-called standard form of "ax+bi"

Answer 9

thanks