complex numbers Word Scramble
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| 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 |
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