complex number addition
Author: Mike Shepperd

z_1 + z_2

- z_2

z_1

z_1 - z_2

z_1 + z_2

z_1 - z_2

- z_1

z_2

z_2 - z_1

z_2 - z_1

z_2 = (3.058711456315789, 3.857270176147482)
u = ComplexVector(z_2)
z_1 = (4.924879718929488, -3.229975585239376)
v = ComplexVector(z_1)
C = ComplexAddition(z_1, z_2)
z = ComplexVector(C)
b = Segment(z_1, C)
a = Segment(z_2, C)
A: -(z_2)
B = (0, 0)
w = Vector(B, A)
D: -(z_2) + z_1
c = Vector(A, D)
d = Vector(B, D)
e = true
f = false
E: -(z_1)
g = Vector(B, E)
F: -(z_1) + z_2
h = Vector(E, F)
i = Vector(B, F)
j = false

Tool: ComplexDiv
Input: A, B
Output: C

c: x(B)^(2.0) + y(B)^(2.0)
C: ((x(A) * x(B) + y(A) * y(B)) / c, (y(A) * x(B) - x(A) * y(B)) / c)

Tool: ComplexMultiplication
Input: A, B
Output: C

C: (x(A) * x(B) - y(A) * y(B), x(A) * y(B) + x(B) * y(A))

Tool: ComplexConjugate
Input: A
Output: E

E: (x(A), -y(A))

Tool: ComplexInverse
Input: A
Output: B

B: (x(A) / (x(A)^(2.0) + y(A)^(2.0)), -y(A) / (x(A)^(2.0) + y(A)^(2.0)))

Tool: ComplexSqrt
Input: A
Output: B, C

d = If(sgn(y(A)) ≟ 0.0, 1.0, sgn(y(A)))
c: sqrt(x(A)^(2.0) + y(A)^(2.0))
C: (-sqrt((c + x(A)) / 2.0), -(d) * sqrt((c - x(A)) / 2.0))
B: (sqrt((c + x(A)) / 2.0), d * sqrt((c - x(A)) / 2.0))

Tool: ComplexAddition
Input: A, B
Output: C

C: A + B

Tool: ComplexSubtraction
Input: A, B
Output: C

C: A - B

Tool: ComplexSquare
Input: A
Output: B

B = ComplexMultiplication(A, A)

Tool: ComplexVector
Input: A
Output: u

u = Vector((0.0, 0.0), A)

Tool: ComplexPowers
Input: A
Output: B, C, D, E, F, G, H, I, J, K, L, M, N, O

B = ComplexSquare(A)
C = ComplexMultiplication(B, A)
D = ComplexMultiplication(C, A)
E = ComplexMultiplication(D, A)
F = ComplexMultiplication(E, A)
G = ComplexMultiplication(F, A)
H = ComplexMultiplication(G, A)
I = ComplexMultiplication(A, H)
J = ComplexMultiplication(A, I)
K = ComplexMultiplication(A, J)
L = ComplexMultiplication(A, K)
M = ComplexMultiplication(A, L)
N = ComplexMultiplication(A, M)
O = ComplexMultiplication(A, N)