Atkin
Quiz #6 Math 144
Tuesday, July 23, 2013
Name:
1. Sketch the graph of the polar equation r  2sin   2cos by making a table of values with
at least 4 points and plotting those points, then finishing with a calculator.
2. Sketch the graph of the polar equation r  3  2sin  by making a table of values with at
least 4 points and plotting those points, then finishing with a calculator.
3. Write the complex number z  2 3  2i in polar form with argument  between 0 and 2 .
4. Graph the complex number z  1 
3
i and find its modulus.
3
Im
Re

 
3
3

5. Multiply  cos  i sin    cos
 i sin
4
4 
4
4

6. Divide

 . Write the answer in polar form.

4  cos120  i sin120 
. Write the answer in polar form.
2  cos 30  i sin 30 
7. Find the indicated power using De Moivre’s Theorem: z n  r n  cos n  i sin n  . Write the
answer in standard form. 1  i 
8
8. Find the three cube roots of i. Write the answer in polar form. Use De Moivre’s Theorem for
    2 k 
   2 k  
Roots: k  r1 n cos 
  i sin 
 for k  0, 1, 2, , n  1, and n  1 .
n 
n  

 
9. Sketch the graph of the parametric equations x  t 2 , y  t  2, for 2  t  4 by making a table
of values with at least 3 points, plotting those points, then finishing the graph with a
y
calculator.
x
1
10. Eliminate the parameter. x  , y  t  1 .
t