Números Complejor
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 ) ⋅ ...
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