MATH PROJECT

MATH PROJECT
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  • Hey Niall, did you understand today's lesson about complex numbers. If you did can you help me?
  • Sure!
  • What is a complex number?
  • A Complex Number is a combination of a Real Number and an Imaginary Number.
  • ohh! And how do we add them.
  • To add two complex numbers we add each part separately for example  (4+5i) + (2+3i) (4+2) + (5i+3i)=6+8i and we do the same with subtracting.
  • for example (4+5i) - (2+3i) (4-2) - (5i-3i)=2-2i
  • Oh and is it the same with multiplying and dividing. 
  • NO. To multiply complex numbers: Each part of the first complex number gets multiplied by each part of the second complex number Just use "FOIL", which stands for "Firsts, Outers, Inners, Lasts"
  • Like this: Example: (4 + 2i)(2+ 7i) (3 + 2i)(1 + 7i)= 3×1 + 3×7i + 2i×1+ 2i×7i  = 3 + 21i + 2i + 14i2  = 3 + 21i + 2i − 14  (because i2 = −1)  = −11 + 23i
  • Oh and what about division?
  • The trick for dividing is to multiply both top and bottom by the conjugate of the bottom.
  • 2 + 3i4 − 5i Multiply top and bottom by the conjugate of 4 − 5i : 2 + 3i4 − 5i×4 + 5i4 + 5i  =  8 + 10i + 12i + 15i216 + 20i − 20i − 25i2 Now remember that i2 = −1, so: =  8 + 10i + 12i − 1516 + 20i − 20i + 25 Add Like Terms (and notice how on the bottom 20i − 20i cancels out!): =  −7 + 22i41 Lastly we should put the answer back into a + bi form: =  −7 41 + 2241i DONE!
  • Thank you! Now I understand complex numbers.
  • That's it!
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