MATH PROJECT

Updated: 12/4/2018

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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!