Help
Options
Didn't know it?
click below
click below
Knew it?
click below
click below
Don't Know
Remaining cards (0)
Know
retry
shuffle
restart
0:00
Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.
Normal Size Small Size show me how
Normal Size Small Size show me how
complex numbers
Chapter 1 - Complex numbers
| Term | Definition |
|---|---|
| The imaginary unit | i = sqrt(-1) |
| "real" numbers definition | non-imaginary numbers |
| "imaginary" numbers definition | numbers defined only in terms of i |
| complex numbers definition | a number that has real and imaginary parts |
| general form of a complex number | z = a + bi |
| addition of complex numbers | z1 + z2 = a + bi + c + di = (a+ c) + (b + d)i |
| multiplication of complex numbers | z1z2 = (a + bi)(c + di) = ac + (ad + bc)i - bd |
| summation of 2 squares formula | a^2 + b^2 = (a + bi)(a - bi) |
| i^n function | has period 4, i -> -1 -> -i -> 1 |
| the complex conjugate of z | if z = a + bi, z* = z - bi |
| complex division | equivilant to realising the denominator, multiply the numerator/denominator by the complex conjugate of the denominator |
| solving for z | let z = a + bi, expand as necessary. Form 2 equations from the real and imaginary parts and solve simutaniously |
| quadratic in terms of its roots | x^2 -(Alpha + Beta)x + (AlphaBeta) |
| sum of the roots of a quadratic | Alpha + Beta = -b/a |
| multiplication of the roots of a quadratic | AlphaBeta = c/a |
| imaginary roots | complex roots of a polynomial with real co-effecients always come in conjugate pairs |
| General roots | Σα = -b/a Σαβ = c/a Σαβγ = -d/a Σαβγδ = e/a etc |
Created by:
That cool NAMe
Popular Math sets