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Products and Quotients of Complex Numbers definitions

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  • Complex Number
    A value expressed as a combination of a real part and an imaginary part, often written in rectangular or polar form.
  • Polar Form
    A representation using a modulus and an angle, typically written as r cis θ or r(cos θ + i sin θ).
  • Rectangular Form
    A way to express a value as a sum of real and imaginary components, usually as a + bi.
  • Modulus
    The distance from the origin to the point representing a value in the complex plane, denoted as r in polar form.
  • Argument
    The angle measured from the positive real axis to the line representing a value in the complex plane, denoted as θ.
  • cis Notation
    A shorthand for cos θ + i sin θ, allowing compact expression of values in polar form.
  • Product
    The result of multiplying two values, found by multiplying moduli and adding arguments in polar form.
  • Quotient
    The result of dividing two values, found by dividing moduli and subtracting arguments in polar form.
  • Multiplication Rule
    A process involving multiplying moduli and adding arguments to combine two values in polar form.
  • Division Rule
    A process involving dividing moduli and subtracting arguments to separate two values in polar form.
  • Angle Addition
    A step in multiplication where the arguments of two values are summed to find the new argument.
  • Angle Subtraction
    A step in division where the argument of the divisor is subtracted from the argument of the dividend.
  • Radian
    A unit for measuring angles, often used in polar form, where π radians equals 180 degrees.
  • Degree
    A unit for measuring angles, commonly used alongside radians in polar representations.
  • Complex Plane
    A two-dimensional plane where the horizontal axis represents real parts and the vertical axis represents imaginary parts.