multiplication of complex numbers
Author: Mike Shepperd

Show z_2

Show z_1

Show z1_z2

z_1+z_2

Show z_1 + z_2

z_2

z_1

Show Parallelogram of Vectors

z_2 = (3.163552369945772, 2.1169110098897628)
u = ComplexVector(z_2)
z_1 = (-0.5687841552816267, 3.1443519634635972)
v = ComplexVector(z_1)
A = ComplexMultiplication(z_1, z_2)
w = ComplexVector(A)
B = (0, 0)
C = Point(xAxis)
D = Point(xAxis)
E = Point(u)
α = Angle(D, E, z_1)
β = Angle(D, E, z_2)
γ = Angle(D, E, A)
distanceEA = Distance(E, A)
a = Distance(E, A)
TextEA: " \,  \, " + a
distanceEz1 = Distance(E, z_1)
TextEz1: " \, \, " + distanceEz1
distanceEz2 = Distance(E, z_2)
TextEz2: " \,  \, " + distanceEz2
b = false
c = false
d = false
F: z_1 + z_2
z = Vector(E, F)
e = false
f = Vector(z_1, F)
g = Vector(z_2, F)
h = 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)