ashking1
  • ashking1
can someone help me Write the expression in standard form.
Mathematics
chestercat
  • chestercat
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ashking1
  • ashking1
\[\frac{ 5 }{ 3-15i }\]
anonymous
  • anonymous
standard form is ax+by=c
anonymous
  • anonymous
standrd form should be a + bi

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anonymous
  • anonymous
Oh I am thinking of a graph yeah I think you are right @d3v13
anonymous
  • anonymous
so basically multiply both the sides by something to get that form
ashking1
  • ashking1
so what do i multiply it by
DanJS
  • DanJS
(3 + 15i )/(3 + 15i) recall i^2 = -1
DanJS
  • DanJS
\[\frac{ 5 }{ (3-15i )}*\frac{ (3 + 15i) }{ (3 + 15i) } =\]
DanJS
  • DanJS
You don't want an imaginary number in the bottom, so switch the sign and multiply by the conjugate thing
DanJS
  • DanJS
you good ?
ashking1
  • ashking1
oa ya but how does that equal to a fraction \[\frac{ 5 }{ 78 } -\frac{ 25 }{ 78}i\] \[\frac{ 5 }{ 78 } +\frac{ 25 }{ 78}i\] \[-\frac{ 5 }{ 78 } +\frac{ 25 }{ 78}i\] \[-\frac{ 5 }{ 78 } -\frac{ 25 }{ 78}i\] these are my choices
DanJS
  • DanJS
you need to multiply those two fractions ...
DanJS
  • DanJS
\[\frac{ 5(3+15i) }{ (3-15i)(3+15i) }=\]
DanJS
  • DanJS
remember i^2 = -1
DanJS
  • DanJS
\[\frac{ 5(3+15i) }{ (3-15i)(3+15i) }= \frac{ 15 + 75 i }{9 -15i + 15i -225*(-1) } =\]
DanJS
  • DanJS
whats next?
ashking1
  • ashking1
ok i got that
DanJS
  • DanJS
\[\frac{ 15 + 75i }{ 234 }\]
DanJS
  • DanJS
just have to reduce the fractions.
ashking1
  • ashking1
\[\frac{ 15 + 75 i }{9 + 225 }\]
ashking1
  • ashking1
234 sorry
DanJS
  • DanJS
\[\frac{ 15 + 75i }{ 234 } = \frac{ 15 }{ 234 } + \frac{ 75i }{ 234 }\]
ashking1
  • ashking1
simplify
DanJS
  • DanJS
yes, just reduce the fractions
ashking1
  • ashking1
\[\frac{ 5 }{ 78 } +\frac{ 25 }{ 78}i\]
DanJS
  • DanJS
yep, standard form --- a + b*i
ashking1
  • ashking1
thanks
DanJS
  • DanJS
welcome

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