By Kardi Teknomo, PhD .
ComplexNumber


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If we have two complex numbers Complex Number Tutorial: Complex Multiplication and Complex Number Tutorial: Complex Multiplication then we can multiply them together and Complex Number Tutorial: Complex Multiplication then we can multiply them together then we can multiply them together

Complex Number Tutorial: Complex Multiplication

Example

Complex Number Tutorial: Complex Multiplication and Complex Number Tutorial: Complex Multiplication and Complex Number Tutorial: Complex Multiplication

Complex Number Tutorial: Complex Multiplication

It is simpler to represent complex multiplication in polar form. If Complex Number Tutorial: Complex Multiplication and Complex Number Tutorial: Complex Multiplication then and Complex Number Tutorial: Complex Multiplication then then

Complex Number Tutorial: Complex Multiplication

  • The magnitude is Complex Number Tutorial: Complex Multiplication . Multiplication of two complex number produces magnitude of the product length of the two factors. . Multiplication of two complex number produces magnitude of the product length of the two factors.
  • The direction is Complex Number Tutorial: Complex Multiplication . Multiplication of two complex number produces sum of angles of the two factors. . Multiplication of two complex number produces sum of angles of the two factors.

Graphically, complex multiplication is represented by polar form representation illustrated below. Geometrically multiplying a complex number Complex Number Tutorial: Complex Multiplication with a complex number Complex Number Tutorial: Complex Multiplication will scale the length of Complex Number Tutorial: Complex Multiplication by the amount of Complex Number Tutorial: Complex Multiplication and then rotate it with amount of Complex Number Tutorial: Complex Multiplication about the origin counterclockwise. with a complex number Complex Number Tutorial: Complex Multiplication will scale the length of Complex Number Tutorial: Complex Multiplication by the amount of Complex Number Tutorial: Complex Multiplication and then rotate it with amount of Complex Number Tutorial: Complex Multiplication about the origin counterclockwise. will scale the length of Complex Number Tutorial: Complex Multiplication by the amount of Complex Number Tutorial: Complex Multiplication and then rotate it with amount of Complex Number Tutorial: Complex Multiplication about the origin counterclockwise. by the amount of Complex Number Tutorial: Complex Multiplication and then rotate it with amount of Complex Number Tutorial: Complex Multiplication about the origin counterclockwise. and then rotate it with amount of Complex Number Tutorial: Complex Multiplication about the origin counterclockwise. about the origin counterclockwise.

Complex Number Tutorial: Complex Multiplication

Complex Number Calculator

First number: real part imaginary part Second number: real part imaginary part Operation

Properties of Complex Multiplication

  • Commutative Complex Number Tutorial: Complex Multiplication
  • Associative Complex Number Tutorial: Complex Multiplication
  • Distributive Complex Number Tutorial: Complex Multiplication
  • Complex number Complex Number Tutorial: Complex Multiplication is the identity element of complex multiplication because Complex Number Tutorial: Complex Multiplication . is the identity element of complex multiplication because Complex Number Tutorial: Complex Multiplication . .
  • Factor theorem: the product of two complex number cannot be zero unless at least one of the two is itself a zero. If Complex Number Tutorial: Complex Multiplication is zero complex number, then Complex Number Tutorial: Complex Multiplication implies either Complex Number Tutorial: Complex Multiplication or Complex Number Tutorial: Complex Multiplication , or both. is zero complex number, then Complex Number Tutorial: Complex Multiplication implies either Complex Number Tutorial: Complex Multiplication or Complex Number Tutorial: Complex Multiplication , or both. implies either Complex Number Tutorial: Complex Multiplication or Complex Number Tutorial: Complex Multiplication , or both. or Complex Number Tutorial: Complex Multiplication , or both. , or both.
  • Multiplication of a real number with a complex number will affect both real and imaginary part. Let Complex Number Tutorial: Complex Multiplication be a real number and Complex Number Tutorial: Complex Multiplication is a complex number. Then, Complex Number Tutorial: Complex Multiplication be a real number and Complex Number Tutorial: Complex Multiplication is a complex number. Then, Complex Number Tutorial: Complex Multiplication is a complex number. Then, Complex Number Tutorial: Complex Multiplication
  • Multiplication of imaginary number Complex Number Tutorial: Complex Multiplication with a complex number Complex Number Tutorial: Complex Multiplication produces Complex Number Tutorial: Complex Multiplication which geometrically means a counterclockwise rotation by a right angle. with a complex number Complex Number Tutorial: Complex Multiplication produces Complex Number Tutorial: Complex Multiplication which geometrically means a counterclockwise rotation by a right angle. produces Complex Number Tutorial: Complex Multiplication which geometrically means a counterclockwise rotation by a right angle. which geometrically means a counterclockwise rotation by a right angle.

Complex Number Tutorial: Complex Multiplication

See Also : Complex Division , Complex Addition , Complex Subtraction

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