Rectangular Form to Modulus and Argument (Degrees) (Level 1)

This math topic focuses on converting complex numbers from rectangular form to polar form, specifically finding the modulus and the argument in degrees. Each question presents a complex number, and students are required to identify or calculate its modulus (the distance from the origin to the point in the complex plane) and its argument (the angle from the positive real axis to the line that connects the origin to the point), with the angle measured in degrees. The topic is part of a broader unit on complex numbers.

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

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Complex Numbers - Rectangular Form to Modulus and Argument (Degrees) Worksheet

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Complex Numbers - Rectangular Form to Modulus and Argument (Degrees)
1
Find the modulus and argument (r, θ) in degrees of this complex number
A LaTex expression showing -6 + 4i
a A LaTex expression showing (6.4, 39 to the power of \ circ)
b A LaTex expression showing (4.2, 45 to the power of \ circ)
c A LaTex expression showing (6.1, 171 to the power of \ circ)
d A LaTex expression showing (7.2, 146 to the power of \ circ)
e A LaTex expression showing (5.4, 22 to the power of \ circ)
f A LaTex expression showing (6.3, 198 to the power of \ circ)
2
Find the modulus and argument (r, θ) in degrees of this complex number
A LaTex expression showing 5 + 3i
a A LaTex expression showing (5.8, 31 to the power of \ circ)
b A LaTex expression showing (5.1, 79 to the power of \ circ)
c A LaTex expression showing (6.7, 63 to the power of \ circ)
d A LaTex expression showing (4.1, 284 to the power of \ circ)
e A LaTex expression showing (7.8, 50 to the power of \ circ)
f A LaTex expression showing (5.1, 259 to the power of \ circ)
3
Find the modulus and argument (r, θ) in degrees of this complex number
A LaTex expression showing -3 - 3i
a A LaTex expression showing (3.2, 252 to the power of \ circ)
b A LaTex expression showing (4.2, 225 to the power of \ circ)
c A LaTex expression showing (2.8, 225 to the power of \ circ)
d A LaTex expression showing (5.1, 259 to the power of \ circ)
e A LaTex expression showing (4.2, 315 to the power of \ circ)
f A LaTex expression showing (3.2, 288 to the power of \ circ)
4
Find the modulus and argument (r, θ) in degrees of this complex number
A LaTex expression showing -3 - 6i
a A LaTex expression showing (8.5, 225 to the power of \ circ)
b A LaTex expression showing (6.7, 243 to the power of \ circ)
c A LaTex expression showing (7.2, 146 to the power of \ circ)
d A LaTex expression showing (5.4, 202 to the power of \ circ)
e A LaTex expression showing (6.7, 207 to the power of \ circ)
f A LaTex expression showing (8.9, 207 to the power of \ circ)
5
Find the modulus and argument (r, θ) in degrees of this complex number
A LaTex expression showing 5 - 5i
a A LaTex expression showing (8.1, 330 to the power of \ circ)
b A LaTex expression showing (7.6, 337 to the power of \ circ)
c A LaTex expression showing (7.1, 315 to the power of \ circ)
d A LaTex expression showing (10.6, 49 to the power of \ circ)
e A LaTex expression showing (8.6, 36 to the power of \ circ)
f A LaTex expression showing (5.4, 338 to the power of \ circ)
6
Find the modulus and argument (r, θ) in degrees of this complex number
A LaTex expression showing -6 - 6i
a A LaTex expression showing (6.3, 198 to the power of \ circ)
b A LaTex expression showing (5.7, 225 to the power of \ circ)
c A LaTex expression showing (5.7, 135 to the power of \ circ)
d A LaTex expression showing (4, 360 to the power of \ circ)
e A LaTex expression showing (8.5, 225 to the power of \ circ)
f A LaTex expression showing (4.1, 194 to the power of \ circ)
7
Find the modulus and argument (r, θ) in degrees of this complex number
A LaTex expression showing 2 - 4i
a A LaTex expression showing (5.1, 281 to the power of \ circ)
b A LaTex expression showing (6.1, 279 to the power of \ circ)
c A LaTex expression showing (4.5, 297 to the power of \ circ)
d A LaTex expression showing (6.1, 99 to the power of \ circ)
e A LaTex expression showing (6.1, 81 to the power of \ circ)
f A LaTex expression showing (6.3, 288 to the power of \ circ)
8
Find the modulus and argument (r, θ) in degrees of this complex number
A LaTex expression showing -4 - 4i
a A LaTex expression showing (6.7, 207 to the power of \ circ)
b A LaTex expression showing (7.2, 146 to the power of \ circ)
c A LaTex expression showing (2.8, 225 to the power of \ circ)
d A LaTex expression showing (7.8, 130 to the power of \ circ)
e A LaTex expression showing (5.7, 225 to the power of \ circ)
f A LaTex expression showing (4.5, 207 to the power of \ circ)