Polar Form Mathematica

Tutorial for mathematica wolfram language.

Polar form mathematica. The polar form of a complex number expresses a number in terms of an angle θ and its distance from the origin r. Polar form of a complex number. Given a complex number in rectangular form expressed as z x yi we use the same conversion formulas as we do to write the number in trigonometric form. Display with standard or polar axes.

Every complex number written in rectangular form has a unique polar form up to an integer multiple of in its argument. The polar form of a complex number is a shorthand for the exponential form. The principal value of the argument is normally taken to be in the interval. So we can write the polar form of a complex number as.

X rcosθ y rsinθ r x2 y2. Convert cartesian coordinates to polar. Many calculators have a rectangular to polar conversion facility. As numeric objects in radians quantity objects with any angular unit or degree minute second dms lists and strings.

R 2 5 6 has magnitude r 2 2 5 6 2 5 946 and angle given by tan l 5 6 2 π 1 914. X y j r cos θ j sin θ displaystyle x y j r left cos theta j sin theta right x yj r cosθ j sinθ r is the absolute value or modulus of the complex number. Ken levasseur umass lowell march 2011. The polar shorthand for aei theta is a angle theta.

So the only mathematica commands you need are abs and arg. Therefore in polar co ordinates r 5 946 1 914. θ is the argument of the complex number. Get the free convert complex numbers to polar form widget for your website blog wordpress blogger or igoogle.

The wolfram language has fundamental support for both explicit complex numbers and symbolic complex variables. Polar form of complex numbers a complex number is a number that can be put in the form x iy where x and y are real numbers and i is called the imaginary unit where i2 1. Find more mathematics widgets in wolfram alpha. Easily create polar plots.

Angles and polar coordinates representing complex numbers vectors or positions using angles is a fundamental construction in calculus and geometry and many applied areas like geodesy. Note that the angle is between π 2 and π meaning that the vector must lie in the second quadrant. However this creates a discontinuity as moves across the negative real axis.