MI 4 Complex Quiz
Name __________________________
You may use a TI-30 calculator on this exam.
1. Let a  2cis40 and b  cis(50) . Find the following. State your answers in polar form.
a) a3  23 cis(3  40 )  8cis(120 )
b) a 4 ·b4  24 cis(160 )  cis(200 )  16cis(360 )  16
a3 8cis(120 )
c) 2 
 8cis(20 )
b
cis(100 )
2. One of the solutions to the equation z 2  6 z  25  0 is 3  4i . With this information, graph
all of the roots of z 2  6 z  25  0 on the grid below.
Remember that for polynomials with real
coefficients, root come in complexconjugate pairs. So the roots are 3  4i and
3  4i .
3. Find a complex number that you can multiply z with so that z gets rotated 60 degrees
clockwise, if z  2 cis(20 ) . Give your answer in rectangular form.
cis (60 ) 
1
3

i
2 2
MI 4 Complex Quiz
4. Solve for z: 1  i  z  z 
2i
2i
 1z  iz  z  
2i
2i
 iz  
2  i  2  i
2  i 2  i
3  4i
5
 3  4i 
 i  iz   i 

 5 
4  3i
4 3
z
  i
5
5 5
 iz  
5. Solve the equation z 5  16  16 3i . Leave your answers in cis form.
z 5  16  16 3i  32cis(300  360 k )
 z  2cis(60  72 k )
 z  2cis(60 ), 2cis(132 ), 2cis(204 ), 2cis(276 ), 2cis(348 )