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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Complex Numbers - Polar Form (Degrees) to Rectangular Form
1
A LaTex expression showing 6.4(cos(129 to the power of \ circ) + i times sin(129 to the power of \ circ))
Find the rectangular form of this polar form complex number
a A LaTex expression showing -4 + 5i
b A LaTex expression showing -6 + 4i
c A LaTex expression showing -9 + 4i
d A LaTex expression showing -4 + 4i
e A LaTex expression showing -9 + 3i
f A LaTex expression showing -8 + 4i
2
A LaTex expression showing 6.7(cos(243 to the power of \ circ) + i times sin(243 to the power of \ circ))
Find the rectangular form of this polar form complex number
a A LaTex expression showing -5 - 7i
b A LaTex expression showing 5 + 8i
c A LaTex expression showing -5 + 7i
d A LaTex expression showing -3 - 6i
e A LaTex expression showing -5 - 6i
f A LaTex expression showing 5 + 7i
3
A LaTex expression showing 7.8(cos(220 to the power of \ circ) + i times sin(220 to the power of \ circ))
Find the rectangular form of this polar form complex number
a A LaTex expression showing -7 + 7i
b A LaTex expression showing -7 + 6i
c A LaTex expression showing -6 - 5i
d A LaTex expression showing -6 - 6i
e A LaTex expression showing -7 - 7i
f A LaTex expression showing -7 - 6i
4
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 + 3i
b A LaTex expression showing -4 - 3i
c A LaTex expression showing -4 + 2i
d A LaTex expression showing -4 + 1i
e A LaTex expression showing -4 - 1i
f A LaTex expression showing -4 + 4i
5
A LaTex expression showing 5.8(cos(301 to the power of \ circ) + i times sin(301 to the power of \ circ))
Find the rectangular form of this polar form complex number
a A LaTex expression showing -4 + 5i
b A LaTex expression showing -4 + 6i
c A LaTex expression showing 4 - 5i
d A LaTex expression showing 6 - 5i
e A LaTex expression showing -6 + 5i
f A LaTex expression showing 3 - 5i
6
Find the rectangular form of this polar form complex number
A LaTex expression showing 4.5(cos(27 to the power of \ circ) + i times sin(27 to the power of \ circ))
a A LaTex expression showing 4 + 4i
b A LaTex expression showing -3 - 6i
c A LaTex expression showing -2 - 6i
d A LaTex expression showing 4 + 2i
e A LaTex expression showing 4 + 6i
f A LaTex expression showing 3 + 6i
7
A LaTex expression showing 7.2(cos(236 to the power of \ circ) + i times sin(236 to the power of \ circ))
Find the rectangular form of this polar form complex number
a A LaTex expression showing -4 - 8i
b A LaTex expression showing -4 - 5i
c A LaTex expression showing -4 - 4i
d A LaTex expression showing -4 - 6i
e A LaTex expression showing -2 - 4i
f A LaTex expression showing -2 - 6i
8
A LaTex expression showing 5.8(cos(149 to the power of \ circ) + i times sin(149 to the power of \ circ))
Find the rectangular form of this polar form complex number
a A LaTex expression showing 6 + 4i
b A LaTex expression showing -5 - 3i
c A LaTex expression showing -5 + 4i
d A LaTex expression showing -5 + 3i
e A LaTex expression showing 4 + 4i
f A LaTex expression showing 5 + 4i