Two complex numbers
and
are multiplied as follows:
In component form,
 |
(4)
|
(Krantz 1999, p. 1). The special case of a complex number multiplied by a scalar
is then given by
 |
(5)
|
Surprisingly, complex multiplication can be carried out using only three real multiplications,
,
, and
as
Complex multiplication has a special meaning for elliptic
curves.
See also
Complex Addition,
Complex Division,
Complex Exponentiation,
Complex Number,
Complex
Subtraction,
Elliptic Curve,
Imaginary
Part,
Multiplication,
Real
Part,
Sign
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References
Cox, D. A. Primes of the Form x2+ny2: Fermat, Class Field Theory and Complex Multiplication.
New York: Wiley, 1997.Krantz, S. G. Handbook
of Complex Variables. Boston, MA: Birkhäuser, p. 1, 1999.Referenced
on Wolfram|Alpha
Complex Multiplication
Cite this as:
Weisstein, Eric W. "Complex Multiplication."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ComplexMultiplication.html
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