Polar Form of Complex Numbers definitions Flashcards
Polar Form of Complex Numbers definitions
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Polar Form A representation of a complex number using a distance from the origin and an angle with the real axis. Rectangular Form A representation of a complex number as the sum of a real part and an imaginary part, written as x + yi. Modulus The distance from the origin to the point representing a complex number in the complex plane. Argument The angle measured from the positive real axis to the line representing a complex number in the complex plane. Real Part The horizontal component of a complex number, corresponding to its projection on the real axis. Imaginary Part The vertical component of a complex number, corresponding to its projection on the imaginary axis. Pythagorean Theorem A formula used to calculate the modulus of a complex number by taking the square root of the sum of the squares of its real and imaginary parts. Inverse Tangent A function used to determine the argument of a complex number from the ratio of its imaginary and real parts. Quadrant One of four regions in the complex plane, each affecting the calculation of the argument for a complex number. Unit Circle A circle of radius one centered at the origin, used to find exact values for trigonometric functions during conversions. Cosine A trigonometric function used to determine the real part of a complex number in polar form. Sine A trigonometric function used to determine the imaginary part of a complex number in polar form. Distribution The process of multiplying the modulus by the cosine and sine components to convert from polar to rectangular form. Degree Mode A calculator setting that interprets angles in degrees, important for correct argument calculations. Radian A unit of angular measure used in trigonometric calculations, often appearing in polar form expressions.
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