C.R.A.Z.Y. is a 2005 Canadian coming-of-age drama film directed by Jean-Marc Vallée and co-written by Vallée and François Boulay. It tells the story of...

be 1 z = z ¯ z z ¯ = z ¯ | z | 2 = x − y i x 2 + y 2 = x x 2 + y 2 − y x 2 + y 2 i . {\displaystyle {\frac {1}{z}}={\frac {\bar {z}}{z{\bar {z}}}}={\frac...

and z. This angle is called the argument of z. The absolute value r of z is given by r = x 2 + y 2 . {\displaystyle \textstyle r={\sqrt {x^{2}+y^{2}}}...

L − d L c L c L d L a L − b L d L − c L b L a L ) ( a R − b R − c R − d R b R a R d R − c R c R − d R a R b R d R c R − b R a R ) ( w x y z ) , {\displaystyle...

express support for the invasion. Z with diacritics: Ź ź Ẑ ẑ Ž ž Ż ż Ẓ ẓ Ẕ ẕ Ƶ ƶ ᵶ Ᶎ ᶎ Ⱬ ⱬ ß : German letter regarded as a ligature of long s (ſ) and short...

{c}},\ q=r^{2}-|c|^{2}} , since | z − c | 2 = z z ¯ − c ¯ z − c z ¯ + c c ¯ {\displaystyle |z-c|^{2}=z{\overline {z}}-{\overline {c}}z-c{\overline {z}}+c{\overline...

\left(t-{\frac {vx}{c^{2}}}\right)\\x'&=\gamma \left(x-vt\right)\\y'&=y\\z'&=z\end{aligned}}} where (t, x, y, z) and (t′, x′, y′, z′) are the coordinates...

namely, A x 2 + B y 2 + C z 2 + F x y + G y z + H x z + J x + K y + L z + M = 0 , {\displaystyle Ax^{2}+By^{2}+Cz^{2}+Fxy+Gyz+Hxz+Jx+Ky+Lz+M=0,} where A, B...

\left(x,y\right)\in R\qquad } ( x , y ) ∈ R ∧ ( x , z ) ∈ R ⟹ y = z {\displaystyle (x,y)\in R\land (x,z)\in R\implies y=z\qquad } Partial functions are defined...

assemble a matrix. 2 [ Q x x − M x x + Q x x Y x x + Q x y Y x y Q x y − M x y + Q x x Y x y + Q x y Y y y Q y x − M y x + Q y x Y x x + Q y y Y x y Q y y −...

c("X", "Y", "Z") # Set the column names of new_df as X, Y, and Z. > print(new_df) # Print the current results. X Y Z A 2 6 12 B 20 30 42 > new_df$Z #...

+ y , − z ) ( + x , − y , − z ) ( − x , + y , − z ) ( − x , − y , + z ) ( − x , − y , − z ) {\displaystyle {\begin{aligned}(+x,+y,+z)&&(-x,+y,+z)&&(+x...

formulas ( z k ) ≈ ( − 1 ) k Γ ( − z ) k z + 1 and ( z + k k ) = k z Γ ( z + 1 ) ( 1 + z ( z + 1 ) 2 k + O ( k − 2 ) ) {\displaystyle {z \choose k}\approx...

plane as the complex numbers c {\displaystyle c} for which the function f c ( z ) = z 2 + c {\displaystyle f_{c}(z)=z^{2}+c} does not diverge to infinity...

equation f ( x , y , z ) = a ( x 2 + y 2 + z 2 ) + 2 ( b x + c y + d z ) + e = 0 {\displaystyle f(x,y,z)=a(x^{2}+y^{2}+z^{2})+2(bx+cy+dz)+e=0} has no real...

⁡ z < 0 , J α ( z ) ∼ 1 2 π z e − i ( z − α π 2 − π 4 ) for  0 < arg ⁡ z < π , Y α ( z ) ∼ − i 1 2 π z e i ( z − α π 2 − π 4 ) for  − π < arg ⁡ z < 0...

r = | z | = x 2 + y 2 . {\displaystyle r=|z|={\sqrt {x^{2}+y^{2}}}.} So the three quantities, r, x and y are related by the Pythagorean equation, r 2...

z: ∫ arcsin ⁡ ( z ) d z = z arcsin ⁡ ( z ) + 1 − z 2 + C ∫ arccos ⁡ ( z ) d z = z arccos ⁡ ( z ) − 1 − z 2 + C ∫ arctan ⁡ ( z ) d z = z arctan ⁡ ( z )...

function f ( x , y , z ) = 2 x + 3 y 2 − sin ⁡ ( z ) {\displaystyle f(x,y,z)=2x+3y^{2}-\sin(z)} is ∇ f ( x , y , z ) = 2 i + 6 y j − cos ⁡ ( z ) k . {\displaystyle...

statistics) r ( Y , Y ^ ) = ∑ i ( Y i − Y ¯ ) ( Y ^ i − Y ¯ ) ∑ i ( Y i − Y ¯ ) 2 ⋅ ∑ i ( Y ^ i − Y ¯ ) 2 = ∑ i ( Y i − Y ^ i + Y ^ i − Y ¯ ) ( Y ^ i − Y ¯ )...

− W 0 ( Y e Y ) = Y − W 0 ( Y e Y ) for  Y < − 1 , W 0 ( Y e Y ) − W − 1 ( Y e Y ) = Y − W − 1 ( Y e Y ) for  − 1 < Y < 0. {\displaystyle X(Y...

t u r + u r ∂ r u r + u z ∂ z u r ) = − ∂ r p + μ ( 1 r ∂ r ( r ∂ r u r ) + ∂ z 2 u r − u r r 2 ) + ρ g r ρ ( ∂ t u z + u r ∂ r u z + u z ∂ z u z ) =...

coordinates is J − 1 = ( x r y r z r x z r 2 x 2 + y 2 y z r 2 x 2 + y 2 − ( x 2 + y 2 ) r 2 x 2 + y 2 − y x 2 + y 2 x x 2 + y 2 0 ) . {\displaystyle...

z {\displaystyle z} -axis, I C , sphere = ∫ − R R 1 2 π ρ r ( z ) 4 d z = ∫ − R R 1 2 π ρ ( R 2 − z 2 ) 2 d z = 1 2 π ρ [ R 4 z − 2 3 R 2 z 3 + 1 5 z...

components ( x , y , z ) ∈ R 3 {\displaystyle (x,y,z)\in \mathbb {R} ^{3}} , r = | r | {\displaystyle r=|\mathbf {r} |} , and a = z ^ − λ 2 ( x ^ + i y ^ ) + 1...

part: Γ ( z ) = ∫ 0 ∞ t z − 1 e − t  d t ,   ℜ ( z ) > 0 . {\displaystyle \Gamma (z)=\int _{0}^{\infty }t^{z-1}e^{-t}{\text{ d}}t,\ \qquad \Re (z)>0\,.}...

identities e x + y = e x e y {\displaystyle e^{x+y}=e^{x}e^{y}} and e y ln ⁡ x = x y , {\displaystyle e^{y\ln x}=x^{y},} one gets z w = ρ c e − d ( θ + 2...

 for all  x , y ∈ X  and  z ∈ [ x , y ] . {\displaystyle \|x-y\|=\|x-z\|+\|z-y\|{\text{ for all }}x,y\in X{\text{ and }}z\in [x,y].} Two norms ‖ ⋅ ‖ α {\displaystyle...

⁡ z = sin ⁡ x cosh ⁡ y + i cos ⁡ x sinh ⁡ y , cos ⁡ z = cos ⁡ x cosh ⁡ y − i sin ⁡ x sinh ⁡ y . {\displaystyle {\begin{aligned}\sin z&=\sin x\cosh y+i\cos...

Assuming r = ( x , y , z ) = x 1 a 1 a 1 + x 2 a 2 a 2 + x 3 a 3 a 3 , {\displaystyle \mathbf {r} =(x,y,z)=x_{1}{\frac {\mathbf {a} _{1}}{a_{1}}}+x_{2}{\frac...