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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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Math worksheet on 'Complex Numbers - Rectangular Form to Polar Form (Degrees) (Level 1)'. Part of a broader unit on 'Complex Numbers' Learn online: app.mobius.academy/math/units/complex_numbers/
1
Find the polar form in degrees of this complex number
A LaTex expression showing -3 + 3i
a A LaTex expression showing 3.7(cos(32 to the power of \ circ) + i times sin(32 to the power of \ circ))
b A LaTex expression showing 5.2(cos(51 to the power of \ circ) + i times sin(51 to the power of \ circ))
c A LaTex expression showing 5.4(cos(349 to the power of \ circ) + i times sin(349 to the power of \ circ))
d A LaTex expression showing 4.2(cos(135 to the power of \ circ) + i times sin(135 to the power of \ circ))
e A LaTex expression showing 3.2(cos(360 to the power of \ circ) + i times sin(360 to the power of \ circ))
f A LaTex expression showing 5.6(cos(21 to the power of \ circ) + i times sin(21 to the power of \ circ))
2
Find the polar form in degrees of this complex number
A LaTex expression showing 5 + 3i
a A LaTex expression showing 8.1(cos(338 to the power of \ circ) + i times sin(338 to the power of \ circ))
b A LaTex expression showing 5.8(cos(211 to the power of \ circ) + i times sin(211 to the power of \ circ))
c A LaTex expression showing 5.8(cos(31 to the power of \ circ) + i times sin(31 to the power of \ circ))
d A LaTex expression showing 7.5(cos(337 to the power of \ circ) + i times sin(337 to the power of \ circ))
e A LaTex expression showing 9.1(cos(354 to the power of \ circ) + i times sin(354 to the power of \ circ))
f A LaTex expression showing 5.1(cos(349 to the power of \ circ) + i times sin(349 to the power of \ circ))
3
Find the polar form in degrees of this complex number
A LaTex expression showing -5 + 4i
a A LaTex expression showing 6.3(cos(72 to the power of \ circ) + i times sin(72 to the power of \ circ))
b A LaTex expression showing 7.1(cos(82 to the power of \ circ) + i times sin(82 to the power of \ circ))
c A LaTex expression showing 6.4(cos(141 to the power of \ circ) + i times sin(141 to the power of \ circ))
d A LaTex expression showing 8(cos(90 to the power of \ circ) + i times sin(90 to the power of \ circ))
e A LaTex expression showing 5.8(cos(59 to the power of \ circ) + i times sin(59 to the power of \ circ))
f A LaTex expression showing 7.9(cos(63 to the power of \ circ) + i times sin(63 to the power of \ circ))
4
Find the polar form in degrees of this complex number
A LaTex expression showing -6 - 6i
a A LaTex expression showing 12.5(cos(355 to the power of \ circ) + i times sin(355 to the power of \ circ))
b A LaTex expression showing 12.8(cos(14 to the power of \ circ) + i times sin(14 to the power of \ circ))
c A LaTex expression showing 8.5(cos(225 to the power of \ circ) + i times sin(225 to the power of \ circ))
d A LaTex expression showing 12.8(cos(342 to the power of \ circ) + i times sin(342 to the power of \ circ))
e A LaTex expression showing 11(cos(27 to the power of \ circ) + i times sin(27 to the power of \ circ))
f A LaTex expression showing 9.2(cos(327 to the power of \ circ) + i times sin(327 to the power of \ circ))
5
Find the polar form in degrees of this complex number
A LaTex expression showing -4 + 4i
a A LaTex expression showing 3.2(cos(321 to the power of \ circ) + i times sin(321 to the power of \ circ))
b A LaTex expression showing 3.5(cos(360 to the power of \ circ) + i times sin(360 to the power of \ circ))
c A LaTex expression showing 5.7(cos(135 to the power of \ circ) + i times sin(135 to the power of \ circ))
d A LaTex expression showing 4.5(cos(42 to the power of \ circ) + i times sin(42 to the power of \ circ))
e A LaTex expression showing 6.3(cos(108 to the power of \ circ) + i times sin(108 to the power of \ circ))
f A LaTex expression showing 1.8(cos(326 to the power of \ circ) + i times sin(326 to the power of \ circ))
6
Find the polar form in degrees of this complex number
A LaTex expression showing 3 + 2i
a A LaTex expression showing 2.2(cos(360 to the power of \ circ) + i times sin(360 to the power of \ circ))
b A LaTex expression showing 3.6(cos(34 to the power of \ circ) + i times sin(34 to the power of \ circ))
c A LaTex expression showing 2.2(cos(63 to the power of \ circ) + i times sin(63 to the power of \ circ))
d A LaTex expression showing 2.4(cos(336 to the power of \ circ) + i times sin(336 to the power of \ circ))
e A LaTex expression showing 3.6(cos(304 to the power of \ circ) + i times sin(304 to the power of \ circ))
f A LaTex expression showing 7.4(cos(54 to the power of \ circ) + i times sin(54 to the power of \ circ))
7
Find the polar form in degrees of this complex number
A LaTex expression showing 3 - 3i
a A LaTex expression showing 3.6(cos(344 to the power of \ circ) + i times sin(344 to the power of \ circ))
b A LaTex expression showing 4.2(cos(315 to the power of \ circ) + i times sin(315 to the power of \ circ))
c A LaTex expression showing 1(cos(72 to the power of \ circ) + i times sin(72 to the power of \ circ))
d A LaTex expression showing 3.5(cos(17 to the power of \ circ) + i times sin(17 to the power of \ circ))
e A LaTex expression showing 3.1(cos(41 to the power of \ circ) + i times sin(41 to the power of \ circ))
f A LaTex expression showing 2.5(cos(337 to the power of \ circ) + i times sin(337 to the power of \ circ))