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Complex Numbers

Rectangular Form to Polar Form (Degrees) (Level 1)

This math topic focuses on converting complex numbers from rectangular form to polar form in degrees. Learners are presented with multiple complex numbers expressed in rectangular form (e.g., 4 - 3i, 3 - 5i, etc.) and are asked to determine their correct polar form representations. Each question offers multiple choice answers, each displaying a complex number in polar form, characterized by a magnitude and an angle in degrees. This exercise is useful for enhancing understanding of complex numbers and their transformations between different algebraic forms.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Complex Numbers - Rectangular Form to Polar Form (Degrees) Worksheet

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Complex Numbers - Rectangular Form to Polar Form (Degrees)
1
Find the polar form in degrees of this complex number
A LaTex expression showing 3 - 5i
a A LaTex expression showing 9(cos(51 to the power of \ circ) + i times sin(51 to the power of \ circ))
b A LaTex expression showing 8.3(cos(75 to the power of \ circ) + i times sin(75 to the power of \ circ))
c A LaTex expression showing 5.8(cos(301 to the power of \ circ) + i times sin(301 to the power of \ circ))
d A LaTex expression showing 9.4(cos(72 to the power of \ circ) + i times sin(72 to the power of \ circ))
e A LaTex expression showing 8(cos(61 to the power of \ circ) + i times sin(61 to the power of \ circ))
f A LaTex expression showing 6.4(cos(290 to the power of \ circ) + i times sin(290 to the power of \ circ))
2
Find the polar form in degrees of this complex number
A LaTex expression showing 4 - 3i
a A LaTex expression showing 5(cos(323 to the power of \ circ) + i times sin(323 to the power of \ circ))
b A LaTex expression showing 4.4(cos(64 to the power of \ circ) + i times sin(64 to the power of \ circ))
c A LaTex expression showing 4.2(cos(315 to the power of \ circ) + i times sin(315 to the power of \ circ))
d A LaTex expression showing 4.1(cos(47 to the power of \ circ) + i times sin(47 to the power of \ circ))
e A LaTex expression showing 3.2(cos(321 to the power of \ circ) + i times sin(321 to the power of \ circ))
f A LaTex expression showing 4(cos(360 to the power of \ circ) + i times sin(360 to the power of \ circ))
3
Find the polar form in degrees of this complex number
A LaTex expression showing -6 - 5i
a A LaTex expression showing 7.6(cos(32 to the power of \ circ) + i times sin(32 to the power of \ circ))
b A LaTex expression showing 7.9(cos(321 to the power of \ circ) + i times sin(321 to the power of \ circ))
c A LaTex expression showing 8.6(cos(44 to the power of \ circ) + i times sin(44 to the power of \ circ))
d A LaTex expression showing 8.6(cos(36 to the power of \ circ) + i times sin(36 to the power of \ circ))
e A LaTex expression showing 7.1(cos(326 to the power of \ circ) + i times sin(326 to the power of \ circ))
f A LaTex expression showing 7.8(cos(220 to the power of \ circ) + i times sin(220 to the power of \ circ))
4
Find the polar form in degrees of this complex number
A LaTex expression showing -3 - 5i
a A LaTex expression showing 5.8(cos(239 to the power of \ circ) + i times sin(239 to the power of \ circ))
b A LaTex expression showing 8.4(cos(346 to the power of \ circ) + i times sin(346 to the power of \ circ))
c A LaTex expression showing 7.5(cos(328 to the power of \ circ) + i times sin(328 to the power of \ circ))
d A LaTex expression showing 6.4(cos(332 to the power of \ circ) + i times sin(332 to the power of \ circ))
e A LaTex expression showing 10.4(cos(11 to the power of \ circ) + i times sin(11 to the power of \ circ))
f A LaTex expression showing 9.4(cos(19 to the power of \ circ) + i times sin(19 to the power of \ circ))
5
Find the polar form in degrees of this complex number
A LaTex expression showing -5 - 4i
a A LaTex expression showing 2.1(cos(283 to the power of \ circ) + i times sin(283 to the power of \ circ))
b A LaTex expression showing 2.6(cos(310 to the power of \ circ) + i times sin(310 to the power of \ circ))
c A LaTex expression showing 4.1(cos(331 to the power of \ circ) + i times sin(331 to the power of \ circ))
d A LaTex expression showing 4.6(cos(360 to the power of \ circ) + i times sin(360 to the power of \ circ))
e A LaTex expression showing 6.4(cos(219 to the power of \ circ) + i times sin(219 to the power of \ circ))
f A LaTex expression showing 5(cos(217 to the power of \ circ) + i times sin(217 to the power of \ circ))
6
Find the polar form in degrees of this complex number
A LaTex expression showing 4 - 4i
a A LaTex expression showing 5.7(cos(315 to the power of \ circ) + i times sin(315 to the power of \ circ))
b A LaTex expression showing 7.2(cos(326 to the power of \ circ) + i times sin(326 to the power of \ circ))
c A LaTex expression showing 11.2(cos(321 to the power of \ circ) + i times sin(321 to the power of \ circ))
d A LaTex expression showing 8.5(cos(304 to the power of \ circ) + i times sin(304 to the power of \ circ))
e A LaTex expression showing 11(cos(213 to the power of \ circ) + i times sin(213 to the power of \ circ))
f A LaTex expression showing 11.9(cos(330 to the power of \ circ) + i times sin(330 to the power of \ circ))
7
Find the polar form in degrees of this complex number
A LaTex expression showing -5 - 3i
a A LaTex expression showing 4.7(cos(12 to the power of \ circ) + i times sin(12 to the power of \ circ))
b A LaTex expression showing 5.5(cos(33 to the power of \ circ) + i times sin(33 to the power of \ circ))
c A LaTex expression showing 4.4(cos(65 to the power of \ circ) + i times sin(65 to the power of \ circ))
d A LaTex expression showing 2.8(cos(47 to the power of \ circ) + i times sin(47 to the power of \ circ))
e A LaTex expression showing 5.8(cos(211 to the power of \ circ) + i times sin(211 to the power of \ circ))
f A LaTex expression showing 5.4(cos(360 to the power of \ circ) + i times sin(360 to the power of \ circ))
8
Find the polar form in degrees of this complex number
A LaTex expression showing 2 - 3i
a A LaTex expression showing 3.6(cos(304 to the power of \ circ) + i times sin(304 to the power of \ circ))
b A LaTex expression showing 4.6(cos(13 to the power of \ circ) + i times sin(13 to the power of \ circ))
c A LaTex expression showing 5.4(cos(326 to the power of \ circ) + i times sin(326 to the power of \ circ))
d A LaTex expression showing 5.8(cos(20 to the power of \ circ) + i times sin(20 to the power of \ circ))
e A LaTex expression showing 5.6(cos(350 to the power of \ circ) + i times sin(350 to the power of \ circ))
f A LaTex expression showing 6.2(cos(40 to the power of \ circ) + i times sin(40 to the power of \ circ))