Products and Quotients of Complex Numbers definitions Flashcards
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.
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