The polar angle for the complex number 0 is indeterminate, but arbitrary choice of the polar angle 0 is common. Hence, the arg function is sometimes considered as multivalued. It can increase by any integer multiple of 2 π and still give the same angle, viewed as subtended by the rays of the positive real axis and from the origin through z. The value of φ is expressed in radians in this article. If the arg value is negative, values in the range (− π, π] or [0, 2 π) can be obtained by adding 2 π. This right over here is in slope intercept form. And it is indeed Y equals negative X minus two. So this is the line that they're reflected about this dashed, purple line. Normally, as given above, the principal value in the interval (− π, π] is chosen. Line segments IN, this is segment IN over here, and TO, this is TO here, are reflected over the line Y is equal to negative X minus two. A reflection is a type of rigid transformation, which means it changes the position or orientation of an image without changing its size or shape. In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation i 2 = − 1 Download our apps here: English / English (United States) © 2023 GeoGebra®. Re is the real axis, Im is the imaginary axis, and i is the " imaginary unit", that satisfies i 2 = −1. Graphing CalculatorCalculator SuiteMath Resources. JSTOR ( July 2022) ( Learn how and when to remove this template message)Ī complex number can be visually represented as a pair of numbers ( a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane.Unsourced material may be challenged and removed. Please help improve this article by adding citations to reliable sources. This article needs additional citations for verification. Move Reflection Line A and Reflection Line B to change the reflection line.
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