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1. Cartesian/Polar Form[A] A complex number can be written in Cartesian Form or Polar form. You must be able to change from one form into the other with confidence.(Cartesian Form) (Polar Form) [B] Steps for changing from Cartesian form to 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 in polar form.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 into Cartesian form.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 a polar object. [B] Trick 1: When you multiply polar objects you add the angles. Example 4If and evaluate zw in the form x + iy.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 find z in the form x + iy.Solution [D] Trick 3: When you divide polar objects you subtract the angles. Example 6Simplify giving your answer in the form x + iy.Solution Example 7Simplify giving your answer in the formSolution [E] Plotting complex numbers in polar form in the Argand diagram. When a complex number is in polar form remember that: 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 in the Argand diagram.Solution |