6.6.3 Practice: Complex Numbers Practice
Precalculus Sem 2
Points Possible:50
Name: Sierra Steadman
Date:
Answer the following questions using what you've learned from this unit. Write your
responses in the space p
...
6.6.3 Practice: Complex Numbers Practice
Precalculus Sem 2
Points Possible:50
Name: Sierra Steadman
Date:
Answer the following questions using what you've learned from this unit. Write your
responses in the space provided.
For questions 1 - 3, the polar coordinates of a point are given. Find the rectangular
coordinates of each point. (2 points each)
1.
For questions 4 - 6, the rectangular coordinates of a point are given. Find the polar
coordinates of each point. (2 points each)
7. a.Give two sets of polar coordinates that could be used to plot the given point. (4
points)
a. (2.5, 8pi/3) and (-2.5, 2pi/3)b. (4, 7pi/2) and (-4, pi/2)8. Identify, graph, and state the symmetries for each polar equation. Write the scale
that you are using for the polar axis. (4 points)
a. r = 9cos(5 ) symmetric about the x-axis
b. r = 2cos9. Transform each polar equation to an equation in rectangular coordinates and
identify its shape. (4 points)
a. = 1.34 radians
theta=tan-1(y/x)=1.35radiansTherefore y/x=tan(1.34radians)
y/x is about 4.26
y=4.26x
The straight line which passes through the origin
b. r = tan sec
r=tan(theta)sec(theta) + r=sin(theta)/cos(theta)x1/cos(theta)
sin(theta)/cos(theta)=tan(theta)=y/x + r=y/x x 1/cos(theta)
rcos(theta)=y/x + y=x^2
parabola
10. Compute the modulus and argument of each complex number. (4 points)
a. -5i
Modulus: |z|=sqrt 0^2 + (-5)^2 = sqrt 25 = 5
Argument: theta=tan-1(-5/0)=tan-1(tan(90))=90 degreesb.
Modulus: r=sqrt 10
Argument: theta=5pi/7
11. Write each complex number in rectangular form. Plot and label (with a - d) each
point on the polar axes below. (4 points)
a.
i
b.
½-sqrt 3/2 i12. Let z = 13 + 7i and w = 3(cos(1.43) + isin(1.43)). (6 points)
a. Convert z to polar form.
14[cos(28)+isin(28)]
b. Calculate zw using De Moivre's theorem.
44.295[cos(1.924)+isin(1.924)]c. Calculate using De Moivre's theorem.
4.931[cos(-0.936)+isin(-0.936)]
For questions 13 - 15, let and .
Calculate the following, keeping your answer in polar form. (2 points each)
13.
s 7pi/6-i sin 7 pi/6)
15.
z1/z2= ¼(cos(29/30)pi-isin(29/30)pi)For questions 16 - 19, write each expression in the standard form for the complex
number a + bi. ( 2 points each)
16.
32+i(32sqrt 3)
18. The complex fifth roots of .
10^(⅕)[cos(11pi/30+8pi/5)+isin(11pi/30+8pi/5)]19. Find all seventh roots of unity and sketch them on the axes below.
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