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

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# Rectangular and Polar Forms (Grades 11-12)

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## 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.