madmerc
  • madmerc
Simplify 4 over -2 - 2i -1 - i -2 - i -1 + i -2 + i
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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Nnesha
  • Nnesha
\[\huge\rm \frac{ 4 }{ -2-2i }\] multiply top and bottom of the fraction by the conjugate of the denominator
madmerc
  • madmerc
what does that mean?
Nnesha
  • Nnesha
do you know what conjugate is ?

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More answers

madmerc
  • madmerc
no
Nnesha
  • Nnesha
conjugate of a +bi is `a-bi` change the sign of imaginary term
Nnesha
  • Nnesha
so what's the conjugate of `-2-2i` ?
madmerc
  • madmerc
-2+2i?
Nnesha
  • Nnesha
right now multiply numerator and denominator by `-2+2i`\[\large\rm \frac{ 4 }{ -2-2i }*\frac{-2+2i}{-2+2i}\]
Nnesha
  • Nnesha
familiar with the distributive property ?
Theloshua
  • Theloshua
lol dude basically you flip the middle sign of the denometer and multiply its by the numerator
Nnesha
  • Nnesha
multiply by both *denominator and numerator *
madmerc
  • madmerc
I still dont understand.
Nnesha
  • Nnesha
it's like rationalize the denominator when we have to move radical sign from bottom to the top
Nnesha
  • Nnesha
to move the imaginary term from the denominator we should multiply top and bottom by the `conjugate ` of the denominator (which is -2-2i)
Nnesha
  • Nnesha
conjugate of -2-2i is `-2+2i` right so now multiply both top and bottom by -2+2i make sense ?
madmerc
  • madmerc
so... 4 and -2+2i times -2+2i?
Nnesha
  • Nnesha
right \[\large\rm \frac{ 4 }{ -2-2i }*\frac{-2+2i}{-2+2i}\] which can be written as \[\large\rm \frac{ 4(-2+2i) }{ (-2-2i)(-2+2i) }\]
madmerc
  • madmerc
then what?
Nnesha
  • Nnesha
now apply distributive property 4(-2+2i) and foil (-2-2i)(-2+2i)
madmerc
  • madmerc
so -8+8i over 4 - 2i ?
Nnesha
  • Nnesha
distributive property \[\rm a(b+c)=a*b+a*c=ab+ac\]
Nnesha
  • Nnesha
-8+8i is correct but how did you get 4-2i ?
Nnesha
  • Nnesha
remember \[\large\rm i= \sqrt{-1} ~~~and ~~~~~~~~~i^2= -1\]
madmerc
  • madmerc
I don't understand the bottom part I tried foil but I don't get it and I need to finish this test
Nnesha
  • Nnesha
how did you foil it. show your work . i'll try to find out the mistake
madmerc
  • madmerc
|dw:1446401983845:dw|
madmerc
  • madmerc
is that right? I just need to finish this please help
Nnesha
  • Nnesha
-2i times -2i = ??
Nnesha
  • Nnesha
remember when we multiply same variables we should add their exponents
Nnesha
  • Nnesha
when we multiply same bases we should `add` exponents \[\huge\rm x^m \times x^n=x^{m+n}\] exponent rule!
madmerc
  • madmerc
so? where are there exponents
madmerc
  • madmerc
i'm so confused
Nnesha
  • Nnesha
just like x is same as x^2 same -2i is sameas -2i^1
Nnesha
  • Nnesha
\[-2i^1 * -2i^1= ?\]
madmerc
  • madmerc
4i^2 ?
Nnesha
  • Nnesha
right and use the fact i^2 = -1
Nnesha
  • Nnesha
replace i^2 with -1
Nnesha
  • Nnesha
|dw:1446402779168:dw|
madmerc
  • madmerc
okay so 4 - 4i^2 ... then what?
Nnesha
  • Nnesha
|dw:1446402947923:dw|
madmerc
  • madmerc
so 4 + 4?
Nnesha
  • Nnesha
correct
Nnesha
  • Nnesha
\[\huge\rm \frac{ \color{ReD}{-8+8i} }{ 8}\] take out the common factor from -8+8i
madmerc
  • madmerc
-1 + i
madmerc
  • madmerc
is that the answer? -1 + i ?
dan815
  • dan815
|dw:1446403304126:dw|
dan815
  • dan815
|dw:1446403388879:dw|
dan815
  • dan815
|dw:1446403453503:dw|
dan815
  • dan815
|dw:1446403560017:dw|

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