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Complex Number

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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Rectangular Form to Polar Form (Degrees)

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Find the polar form in degrees of this complex number

−3−6i-3 - 6i

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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 2 + 3i
a A LaTex expression showing 3.6(cos(56 to the power of \ circ) + i times sin(56 to the power of \ circ))
b A LaTex expression showing 4.3(cos(360 to the power of \ circ) + i times sin(360 to the power of \ circ))
c A LaTex expression showing 5.3(cos(11 to the power of \ circ) + i times sin(11 to the power of \ circ))
d A LaTex expression showing 4.8(cos(24 to the power of \ circ) + i times sin(24 to the power of \ circ))
e A LaTex expression showing 2.8(cos(360 to the power of \ circ) + i times sin(360 to the power of \ circ))
f A LaTex expression showing 4.8(cos(321 to the power of \ circ) + i times sin(321 to the power of \ circ))
2
Find the polar form in degrees of this complex number
A LaTex expression showing -3 - 6i
a A LaTex expression showing 3.1(cos(341 to the power of \ circ) + i times sin(341 to the power of \ circ))
b A LaTex expression showing 3.4(cos(299 to the power of \ circ) + i times sin(299 to the power of \ circ))
c A LaTex expression showing 5.7(cos(298 to the power of \ circ) + i times sin(298 to the power of \ circ))
d A LaTex expression showing 6.7(cos(243 to the power of \ circ) + i times sin(243 to the power of \ circ))
e A LaTex expression showing 6.4(cos(309 to the power of \ circ) + i times sin(309 to the power of \ circ))
f A LaTex expression showing 5(cos(270 to the power of \ circ) + i times sin(270 to the power of \ circ))
3
Find the polar form in degrees of this complex number
A LaTex expression showing 5 + 3i
a A LaTex expression showing 5.8(cos(31 to the power of \ circ) + i times sin(31 to the power of \ circ))
b A LaTex expression showing 9.1(cos(354 to the power of \ circ) + i times sin(354 to the power of \ circ))
c A LaTex expression showing 5.8(cos(211 to the power of \ circ) + i times sin(211 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 5.1(cos(349 to the power of \ circ) + i times sin(349 to the power of \ circ))
f A LaTex expression showing 8.1(cos(338 to the power of \ circ) + i times sin(338 to the power of \ circ))
4
Find the polar form in degrees of this complex number
A LaTex expression showing -6 + 4i
a A LaTex expression showing 8.5(cos(56 to the power of \ circ) + i times sin(56 to the power of \ circ))
b A LaTex expression showing 9.1(cos(310 to the power of \ circ) + i times sin(310 to the power of \ circ))
c A LaTex expression showing 6.8(cos(48 to the power of \ circ) + i times sin(48 to the power of \ circ))
d A LaTex expression showing 7.2(cos(146 to the power of \ circ) + i times sin(146 to the power of \ circ))
e A LaTex expression showing 8.3(cos(303 to the power of \ circ) + i times sin(303 to the power of \ circ))
f A LaTex expression showing 6.8(cos(324 to the power of \ circ) + i times sin(324 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 5(cos(127 to the power of \ circ) + i times sin(127 to the power of \ circ))
b A LaTex expression showing 8(cos(61 to the power of \ circ) + i times sin(61 to the power of \ circ))
c A LaTex expression showing 8.8(cos(307 to the power of \ circ) + i times sin(307 to the power of \ circ))
d A LaTex expression showing 6.4(cos(39 to the power of \ circ) + i times sin(39 to the power of \ circ))
e A LaTex expression showing 10.5(cos(59 to the power of \ circ) + i times sin(59 to the power of \ circ))
f A LaTex expression showing 9.6(cos(321 to the power of \ circ) + i times sin(321 to the power of \ circ))
6
Find the polar form in degrees of this complex number
A LaTex expression showing 4 + 5i
a A LaTex expression showing 8.1(cos(330 to the power of \ circ) + i times sin(330 to the power of \ circ))
b A LaTex expression showing 6.4(cos(51 to the power of \ circ) + i times sin(51 to the power of \ circ))
c A LaTex expression showing 7.3(cos(344 to the power of \ circ) + i times sin(344 to the power of \ circ))
d A LaTex expression showing 8.6(cos(306 to the power of \ circ) + i times sin(306 to the power of \ circ))
e A LaTex expression showing 6.4(cos(39 to the power of \ circ) + i times sin(39 to the power of \ circ))
f A LaTex expression showing 7.8(cos(329 to the power of \ circ) + i times sin(329 to the power of \ circ))
7
Find the polar form in degrees of this complex number
A LaTex expression showing 2 - 5i
a A LaTex expression showing 5.3(cos(50 to the power of \ circ) + i times sin(50 to the power of \ circ))
b A LaTex expression showing 5.9(cos(43 to the power of \ circ) + i times sin(43 to the power of \ circ))
c A LaTex expression showing 5.4(cos(292 to the power of \ circ) + i times sin(292 to the power of \ circ))
d A LaTex expression showing 4.6(cos(300 to the power of \ circ) + i times sin(300 to the power of \ circ))
e A LaTex expression showing 5.3(cos(22 to the power of \ circ) + i times sin(22 to the power of \ circ))
f A LaTex expression showing 6.9(cos(299 to the power of \ circ) + i times sin(299 to the power of \ circ))