anonymous
  • anonymous
someone HELP ME: write the expression as a complex number in standard form. (-1+5i)(6+3i)
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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zzr0ck3r
  • zzr0ck3r
-1*6+(-3i)+30i+15&i^2 -6+27i-15 27i-21
mathstudent55
  • mathstudent55
Here you are multiplying complex numbers. You start out by multiplying with FOIL. (-1 + 5i)(6 + 3i) = = -1 * 6 + (-1) * (3i) + 5i * 6 + 5i * (3i) Now you do the multiplications: = -6 - 3i + 30i + 15i^2 Now you simplify i^2, since i^2 = -1 = -6 - 3i + 30i + 15(-1) Multiply 15 by -1 = -6 - 3i + 30i - 15 Now you combine like terms like we did before. = -6 - 15 - 3i + 30i = -21 + 27i This is standard form for a complex number
zzr0ck3r
  • zzr0ck3r
same thing as(a+b)(c+d) but i^2=-1

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anonymous
  • anonymous
|dw:1370595064687:dw| write the expression as a complex number dividing complex numbers
mathstudent55
  • mathstudent55
In order to simplify this fraction, you must multiply the numerator and denominator of the fraction by the same complex number. The complex number used for this is called the complex conjugate. You need the complex conjugate of the denominator. The complex conujugate of a + bi is a - bi Examples: The complex conjugate of 3 + 5i is 3 - 5i The complex conjufgate of 4 - i is 4 + 1 To get the complex conjugate of a number, just change the sign of the imaginary part.
mathstudent55
  • mathstudent55
What is the complex conjugate of our denominator, 2 - 3i?
anonymous
  • anonymous
2+3i
mathstudent55
  • mathstudent55
Good. Now we multiply both the numerator and the denominator of the fraction by 2 + 3i
mathstudent55
  • mathstudent55
|dw:1370638473667:dw|
mathstudent55
  • mathstudent55
If you need instructions on multiplying two complex numbers together, look up where I explained the previous problem.
mathstudent55
  • mathstudent55
|dw:1370638555070:dw|
mathstudent55
  • mathstudent55
|dw:1370638755940:dw|
mathstudent55
  • mathstudent55
|dw:1370638819871:dw|
anonymous
  • anonymous
ok i got it thank you so much have a good weekend

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