##### Notes

This printable supports Common Core Mathematics Standard HSN-CN.B.4

##### Print Instructions

NOTE: Only your test content will print.
To preview this test, click on the File menu and select Print Preview.

See our guide on How To Change Browser Print Settings to customize headers and footers before printing.

# Rectangular and Polar Forms (Grades 11-12)

Print Test (Only the test content will print)

## Rectangular and Polar Forms

1.
Convert $-4+2i$ to polar form.
1. $2sqrt(5) \ [ \ cos(153.4°) + i sin(153.4°) \ ]$
2. $2sqrt(3) \ [ \ cos(153.4°) + i sin(153.4°) \ ]$
3. $2 sqrt(5) \ [ \ cos(-26.6°) + i sin(-26.6°) \ ]$
4. $2sqrt(3) \ [ \ cos(-26.6°) + i sin(-26.6°) \ ]$
2.
What is the polar form of the complex number $-5 ?$
1. $-5 \ (cos180° + i sin180°)$
2. $5 \ (cos0° + i sin0°)$
3. $5 \ (cos180° + isin180°)$
4. $"This is not a complex number."$
3.
What are the polar coordinates of $2-5i$ to one decimal place?
1. $(5, -68deg)$
2. $(5.4, 68.2deg)$
3. $(5.4, -68.2deg)$
4. $(5, 68deg)$
4.
What are the polar coordinates of $-3+7i$ to one decimal place?
1. $(3.7, -10deg)$
2. $(-7.6, -113.1deg)$
3. $(76, 113deg)$
4. $(7.6, 113.2deg)$
5.
Convert $3sqrt(7) \ (cos80° + i sin80°)$ to rectangular form.
1. $7.8 + 1.4i$
2. $1.4 + 1.0 i$
3. $1.4 + 7.8i$
4. $0.2 + 1.0i$
6.
What is the rectangular form of the complex number whose polar coordinates are $(6, -18°) ?$
1. $5.7 - 0.3 i$
2. $5.7 - 1.9i$
3. $5.7 + 1.9i$
4. $1.9 - 5.7i$
7.
Let the following graph represent the complex plane (assume that x is the real axis and y is the imaginary axis). Let $z = 4+3i$ be the complex number represented by the letter I.
A.
What is the distance from I to the origin? Let $alpha$ represent this value.
1. $alpha = 5$
2. $alpha = 2sqrt(5)$
3. $alpha = 4$
4. $alpha = 3$
B.
If a line is drawn between I and the origin, what is the angle between this line and the positive x-axis, starting from the x-axis and going in a counterclockwise direction? Let $beta$ represent this angle.
1. $beta = 45.0°$
2. $beta = 53.1°$
3. $beta = 36.9°$
4. $beta = 48.6°$
C.
What are the polar coordinates of the complex number $z ?$
1. $(4, 30.2°)$
2. $(5, 36.9°)$
3. $(5, 53.1°)$
4. $(4, 53.1°)$
D.
What is the significance of the answers in parts a and b compared to part c? Choose the best answer.
1. They are similar, since the geometry of the complex plane is closely related to the polar coordinates of a complex number.
2. They are the same. This is only a phenomenon of the first quadrant though; for a complex number in any other quadrant, these values would be different.
3. They are the same, since $alpha$ represents the modulus of $z$, and $beta$ represents the argument of $z.$
4. Any similarity or equality is pure chance; there is no relationship between these values.
You need to be a HelpTeaching.com member to access free printables.