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1. Cartesian/Polar Form![]()
(i) Find ![]() (ii) Draw a little picture to locate the complex number in a quadrant. (iii) Find ![]() (iv) Find q in radians. (v) Change to Polar form. Example 1Find z = -1-1i in polar form.Solution Example 2Write![]() Solution [C] Changing from Polars to Cartesians To change from Polars to Cartesians simply look up the cosine and sine of the angle after changing it from radians into degrees. Remember ASTC. Example 3Put![]() Solution 2. Tricks with the Polar Object[A] When a complex number is in Polar form the first thing students do is to change it back into Cartesians because they are uncomfortable working in Polars. This often makes the problem more difficult.We shall call an object of the form ![]() [B] Trick 1: When you multiply polar objects you add the angles. ![]() ![]() ![]() Example 4If![]() ![]() Solution [C] Trick 2: When you invert a polar object you change the sign between the real and imaginary components. ![]() ![]() ![]() This result is also true for ![]() ![]() Example 5If![]() Solution [D] Trick 3: When you divide polar objects you subtract the angles. ![]() ![]() ![]() ![]() Example 6Simplify![]() Solution Example 7Simplify![]() ![]() Solution [E] Plotting complex numbers in polar form in the Argand diagram. When a complex number is in polar form ![]() r = the distance to the origin (draw a circle of radius r) q = the angle made with the +Re-axis (measure out this angle) Example 8Sketch the complex number![]() Solution |
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