Question

Write the expression in standard form.

\(\large\dfrac{6}{4-13i}\)

Answer 1

\(\large -\dfrac{24}{185}~-~\dfrac{78}{185}i\)

\(\large \dfrac{24}{185}~+~\dfrac{78}{185}i\)

\(\large -\dfrac{24}{185}~+~\dfrac{78}{185}i\)

\(\large \dfrac{24}{185}~-~\dfrac{78}{185}i\)

Answer 2

@thomaster @ganeshie8 @satellite73

Answer 3

\[\large\dfrac{6}{4-13i}\times \frac{4+13i}{4+13i}\] is a start

Answer 4

the denominator will be \(4^2+13^2=185\)

Answer 5

which is the whole point of multiplying by the conjugate
the numerator is whatever you get

Answer 6

why \(13^2\)
wouldn't it be \(13i^2\)

Answer 7

\[(a+bi)(a-bi)=a^2+abi-abi-(bi)^2=a^2+b^2\]

Answer 8

in brief \((a+bi)(a-bi)=a^2+b^2\) a real number

Answer 9

I got \(\large \dfrac{-54}{185}\)

Answer 10

so would it be d?