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Polar coords to rectangular coords how to#

Note that 0.86603 is √3/2, and so the two imaginary roots are (-1±√3)/2. Converting either of them is a one step process involving proportions. It also shows the cube roots of each of these complex numbers. The angle value of a polar coordinate can be given in either degress or radians.

Polar coords to rectangular coords how to#

Real Statistics Functions: The Real Statistics Resource Pack supplies the following functions, where z is a 1 × 2 range which represents a complex number in rectangular format and zz is a 1 × 2 range which represents a complex number in polar format.ĬPolar( z) = 1 × 2 range with z in polar formatĬRect( zz) = 1 × 2 range with zz in rectangular formatĬRoots( z, n) = n × 2 range in which each row represents one of the n unique n th roots of zįigure 1 shows the complex numbers 1, – i and 1 + i, and shows how to convert them to polar format, and then back to rectangular format. It is sufficient to use values of k = 0, 1, …, n-1 to get all n unique roots. Thus, ( r 1/ n, ( θ+kπ)/ n) is also an n th root of ( r, θ). The coordinate system we are most familiar with is called the Cartesian coordinate system, a rectangular plane divided into four quadrants by horizontal and. In the simplest example, Cartesian or rectangular coordinates on the plane locate a point P in terms of two coordinate measurements x and y: how far over and. These can be found by recalling that ( r, θ) is equivalent ( r, θ+kπ) for all integers k. Since r and θ are real numbers, these values can be obtained easily in Excel to find one n th root, but by the Fundamental Theorem of Algebra (see Roots of a Polynomial), there are n such roots. To convert from rectangular coordinates to polar coordinates, use one or more of the formulas: cos x r, sin y r, tan y x, and r x2 + y2. We can find the n th root of a complex number in the same way, namely ( r 1/ n, θ/ n). To convert from polar coordinates to rectangular coordinates, use the formulas x rcos and y rsin. if z is ( r, θ) in polar format, then z n = ( re θi) n = r ne n θi, which is ( r n, nθ), which is ( r n cos( nθ), r n sin( nθ)) in rectangular format, or equivalently (| z| n cos( n

i), some of the operations described in Complex Number Operations are easier to perform using polar notation.

It thus follows that ( c, d) = rcos θ + i rsin θ, which it turns out is equivalent to re θi.īecause of the properties of the exponential function re θi (or similar properties for rcos θ + rsin θ The inverse transformation, converting polar format into rectangular form is accomplished via the formulas c = rcos θ and d = rsin θ which in Excel is c = r*COS( θ) and d = r*SIN( θ) . Polar coordinates are expressed in the form (r, ), where r refers to the distance from the origin to the point and refers to the degree measure of the angle. Note that there are an infinite number of equivalent polar formats in fact, for any integer k, ( c, d) can also be represented by the polar format ( r, θ+ kπ), where π = Pi().

In Excel, this can be expressed by r = SQRT( c^2+ d^2) and θ = ATAN2( c, d). Note that r = |z| (the absolute value) and we use the notation arg r for θ. Complex numbers ( c, d) (in rectangular format) can be converted to polar format ( r, θ) using the formulas r = and θ = arctan( d/ c).