Core Pure Flashcards
(27 cards)
Z + Z* = …
2a
Z x Z* = …
a^(2) + b^(2)
(z - ‘Z’)(z - ‘Z*’) = …
Z^(2) - ZS + P
- S = Z + Z*
- P = Z x Z*
For the complex number (Z), the mod-arg form is…
Z = r(cos(a) + isin(a))
|Z1 + Z2| = …
|Z1| x |Z2|
|Z1 - Z2| = …
|Z1| / |Z2|
arg(Z1 x Z2) = …
arg(Z1) + arg(Z2) = …
arg(Z1 / Z2) = …
arg(Z1) - arg(Z2) = …
What is |Z - a - bi| = r ?
A circle.
What is |Z - a - bi| = |Z - a - bi| ?
A line.
What is arg(Z - a - bi) = a
A half-line.
Where do you shade in |Z - a - bi| < r ?
Inside the Circle.
Where do you shade in |Z - a - bi| > r ?
Outside the circle.
Where do you shade in |Z - a - bi| < |Z - a - bi| ?
Shade the side the inequality arrow points. ( Draw The perpendicular bisector of the line between the points)
Where do you shade in arg(Z - a - bi) < a ?
Shade between the positive x-axis and the half-line.
Where do you shade in arg(Z - a - bi) > a ?
Shade above the half line.
(For roots of polynomials):
a^(2) + b^(2) = …
(Σa)^(2) - 2(Σab)
(For roots of polynomials):
a^(2) + b^(2) + c^(2) = …
(Σa)^(2) - 2(Σab)
(For roots of polynomials):
a^(2) + b^(2) + c^(2) + d^(2) = …
(Σa)^(2) - 2(Σab)
(For roots of polynomials):
a^(3) + b^(3) + c^(3) = …
(Σa)^(3) - 3(Σab)(Σa)
(For roots of polynomials):
a^(3) + b^(3) + c^(3) + d^(3) = …
(Σa)^(3) - 3(Σab)(Σa) + 3(Σabc)
a.b = …
|a||b| x cos(θ)
What is the final statement of a proof by induction?
True for n = 1, if true for n = k, then true for n = k + 1 for all n ∈ ℤ+.
Write the intersection of |z-a| = c and arg(z-a)= b in set notation.
{z ∈ C: |z-a| = c} n {z ∈ C: arg(z-a)= b}
