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### Polar to Rectangular Conversions

```
Date: 4/19/96 at 19:16:1
From: Anonymous
Subject: Polar to Rectangular Conversions

How do I convert "8 cis 30" into rectangular coordinates?
I am totally lost.

Thank you.
```

```
Date: 8/4/96 at 16:22:33
From: Doctor Mike
Subject: Re: Polar to Rectangular Conversions

Hello,

The expression "8 cis 30" is a way of writing the complex number
"8*(cos(30) + i*sin(30))" which  has Real part 8*cos(30) and has
Imaginary part 8*sin(30).  Usually the system of complex numbers
is thought of as a plane, similar to the usual Cartesian plane that
consists of pairs (X,Y) of real numbers.  In this interpretation,
your polar-type expression "8 cis 30" converts to a rectangular
ordered pair (8*cos(30) , 8*sin(30)).  The sine of 30 degrees is
one half, and the cosine of 30 degrees is one half of the square
root of three, so this ordered pair is (4*sqrt(3), 4)

I hope this is the information you needed.

-Doctor Mike,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Equations, Graphs, Translations
High School Imaginary/Complex Numbers

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