Higher mathematics
Complex numbers
Modulus, argument and distance in the complex plane.
Higher mathematics
Complex number modulus
|z| = √(a²+b²)→Higher mathematicsComplex number argument
arg z = atan2(b,a)→Higher mathematicsDistance between complex numbers
|z₁−z₂| = √((a₁−a₂)²+(b₁−b₂)²)→Higher mathematicsReal part of a complex sum
Re(z₁+z₂) = a+c→Higher mathematicsImaginary part of a complex sum
Im(z₁+z₂) = b+d→Higher mathematicsReal part of a complex product
Re(z₁z₂) = ac−bd→Higher mathematicsImaginary part of a complex product
Im(z₁z₂) = ad+bc→Higher mathematicsComplex number addition
z₁ + z₂→Higher mathematicsComplex number subtraction
z₁ − z₂→Higher mathematicsComplex number multiplication
z₁ · z₂→Higher mathematicsComplex number division
z₁ / z₂→Higher mathematicsComplex conjugate
conj(z)→Higher mathematicsComplex modulus from notation
|z|→Higher mathematicsComplex argument from notation
arg z = atan2(Im z, Re z)→Higher mathematicsComplex number power
zⁿ→Higher mathematicsComplex polar form
z = r(cos φ + i sin φ)→