Números Complejor

EJ. 1 EJ. 2

i

17

→i →b −a
2 2

(a2)⋅(i6) + (b2)⋅(i8)

EJ. 3 EJ. 4

( i⋅ x + i⋅ y) ⋅ ( i⋅ x − iy) simplificar → y − x
2 2

2

2 2 2

( i⋅ x + i⋅ y) → ( x⋅ i +y⋅ i) expandir → −x − 2 ⋅ x⋅ y − y
4

EJ. 5

( 1 + i) → −4

EJ. 6

[ ( 3 − 4 ⋅ i) ( 4 + 3 ⋅ i) ] → 24 − 7i

EJ. 7

O := 2 ⋅ i

( 4) + 6 ⋅ ( i 3)

Re( O) = 2 Im( O)= −6
18

EJ. 8

i

−3 i −2i

( 7) + i2⋅(1 + i4)⋅(−i)26 simplificar
= 0.16 + 0.08i

→ 1 + 3i

EJ. 9

−5 − 10i

EJ. 10

M := ( 0.1 −0.2 −0.1 ) Q := ( −0.2 0.1 0.3) P := ( 0.4 0 0.1 )

 −0.3  T  R MQ := ( Q − M ) = 0.3     0.4 
R MQ⋅ RMP = 0.05

 0.3  R MP := ( P − M ) =  0.2     0.2 
T

α :=

( −0.3) + ( 0.3) + (0.4) = 0.583
2 2 2

2

2

2

 −0.02  R MQ × RMP =  0.18     −0.15 
Z := RMQ⋅ RMP = 0.05

β :=

( 0.3) + ( 0.2) + ( 0.2) = 0.412

δ :=

 Z  = 0.208  α⋅ β  

ζ := acos( δ) = 1.361 ζ⋅ 180 π = 77.996

EJ. 13

η := ( 10 −6 5 ) θ := ( 0.1 0.2 0.3 ) ι := κ := ( 10) + ( −6 ) + ( 5) = 12.689 ( 0.1) + ( 0.2) + ( 0.3) = 0.374
2 2 22 2 2

λ := ( 10⋅ 0.1) + ( −6 ⋅ 0.2) + ( 5 ⋅ 0.3) = 1.3

ν := ( ι⋅ κ) = 4.748

Producto punto: "A*B=AxBx + AyBy + AzBz" "A*B=|A||B| cosθ" Componente vectoria paralelo 1Ax-1.2Ay + 1.5Az con 74.108°

"4.748 cos θ =1.3" ξ :=

 λ  = 0.274 ν    = 74.108  π 
180 

( acos( ξ) ) ⋅  

Producto cruz: AxB = |A||B|sin(θ) AxB = i(Ay Bz - Az By) + j(AzBx - Ax Bz ) + k(Ax By - Ay Bx ) Τ := [ ( −6 ⋅ 0.3) − ( 5 ⋅ 0.2) ] + [ ( 5⋅ 0.1) − ( 10⋅ 0.3) ] + [ ( 10⋅ 0.2) − ( −6 ⋅ 0.1) ] = −2.7 Ψ := ( −6 ⋅ 0.3) − ( 5 − 0.2) = −6.6 Χ:= ( 5 ⋅ 0.1) − ( 10⋅ 0.3) = −2.5 Υ := ( 10⋅ 0 − 0.2) − ( −6 ⋅ 0.1) = 0.4 = - 6.6i -2.5j +0.4k

Ο :=

 Τ  = −0.569 ν    = −34.66  π 
180 

asin( Ο ) ⋅  ...