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

This math topic focuses on converting complex numbers from polar form (given in degrees) to rectangular form. Each question presents a complex number in polar form, and students are tasked with identifying the correct rectangular form from multiple choices. The questions challenge students to apply their understanding of the relationship between polar and rectangular complex number representations, enhancing their skills in complex number conversion and trigonometric function manipulation.

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

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

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Math worksheet on 'Complex Numbers - Polar Form (Degrees) to Rectangular Form (Level 1)'. Part of a broader unit on 'Complex Numbers' Learn online: app.mobius.academy/math/units/complex_numbers/
1
Find the rectangular form of this polar form complex number
A LaTex expression showing 5(cos(233 to the power of \ circ) + i times sin(233 to the power of \ circ))
a A LaTex expression showing -4 - 6i
b A LaTex expression showing -4 - 7i
c A LaTex expression showing -2 - 4i
d A LaTex expression showing -2 - 6i
e A LaTex expression showing -2 + 6i
f A LaTex expression showing -3 - 4i
2
A LaTex expression showing 6.3(cos(162 to the power of \ circ) + i times sin(162 to the power of \ circ))
Find the rectangular form of this polar form complex number
a A LaTex expression showing -4 + 3i
b A LaTex expression showing -3 + 4i
c A LaTex expression showing -6 + 2i
d A LaTex expression showing -4 + 4i
e A LaTex expression showing -4 + 2i
f A LaTex expression showing -5 + 4i
3
Find the rectangular form of this polar form complex number
A LaTex expression showing 5(cos(217 to the power of \ circ) + i times sin(217 to the power of \ circ))
a A LaTex expression showing -7 - 3i
b A LaTex expression showing -5 - 3i
c A LaTex expression showing -6 - 3i
d A LaTex expression showing -7 - 1i
e A LaTex expression showing -4 - 3i
f A LaTex expression showing -7
4
Find the rectangular form of this polar form complex number
A LaTex expression showing 5.4(cos(68 to the power of \ circ) + i times sin(68 to the power of \ circ))
a A LaTex expression showing 3 + 6i
b A LaTex expression showing 1 + 6i
c A LaTex expression showing -1 + 6i
d A LaTex expression showing 3 + 5i
e A LaTex expression showing 2 + 5i
f A LaTex expression showing -1 - 6i
5
A LaTex expression showing 3.6(cos(304 to the power of \ circ) + i times sin(304 to the power of \ circ))
Find the rectangular form of this polar form complex number
a A LaTex expression showing 5 - 3i
b A LaTex expression showing 7 - 2i
c A LaTex expression showing 2 - 3i
d A LaTex expression showing 3 - 3i
e A LaTex expression showing 8 - 2i
f A LaTex expression showing 5 - 2i
6
A LaTex expression showing 5.8(cos(329 to the power of \ circ) + i times sin(329 to the power of \ circ))
Find the rectangular form of this polar form complex number
a A LaTex expression showing -5 + 5i
b A LaTex expression showing -6 + 5i
c A LaTex expression showing -5 + 3i
d A LaTex expression showing -6 + 3i
e A LaTex expression showing -5 - 3i
f A LaTex expression showing 5 - 3i
7
A LaTex expression showing 5.7(cos(135 to the power of \ circ) + i times sin(135 to the power of \ circ))
Find the rectangular form of this polar form complex number
a A LaTex expression showing -4 + 4i
b A LaTex expression showing -4 + 3i
c A LaTex expression showing -4 - 3i
d A LaTex expression showing -4 + 1i
e A LaTex expression showing -4 + 2i
f A LaTex expression showing -4 - 1i