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.

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

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Math worksheet on 'Complex Numbers - Rectangular Form to Modulus and Argument (Degrees) (Level 1)'. Part of a broader unit on 'Complex Numbers' Learn online: app.mobius.academy/math/units/complex_numbers/
1
Find the modulus and argument (r, θ) in degrees of this complex number
A LaTex expression showing -5 + 5i
a A LaTex expression showing (7, 360 to the power of \ circ)
b A LaTex expression showing (5, 360 to the power of \ circ)
c A LaTex expression showing (6.1, 171 to the power of \ circ)
d A LaTex expression showing (6.4, 141 to the power of \ circ)
e A LaTex expression showing (7.1, 135 to the power of \ circ)
f A LaTex expression showing (5.1, 169 to the power of \ circ)
2
Find the modulus and argument (r, θ) in degrees of this complex number
A LaTex expression showing -4 - 3i
a A LaTex expression showing (10.8, 248 to the power of \ circ)
b A LaTex expression showing (8.5, 249 to the power of \ circ)
c A LaTex expression showing (5, 217 to the power of \ circ)
d A LaTex expression showing (10.2, 101 to the power of \ circ)
e A LaTex expression showing (8.1, 240 to the power of \ circ)
f A LaTex expression showing (8.9, 243 to the power of \ circ)
3
Find the modulus and argument (r, θ) in degrees of this complex number
A LaTex expression showing -5 + 3i
a A LaTex expression showing (7.8, 50 to the power of \ circ)
b A LaTex expression showing (7.6, 113 to the power of \ circ)
c A LaTex expression showing (5.8, 149 to the power of \ circ)
d A LaTex expression showing (6.4, 129 to the power of \ circ)
e A LaTex expression showing (8.9, 63 to the power of \ circ)
f A LaTex expression showing (8.5, 111 to the power of \ circ)
4
Find the modulus and argument (r, θ) in degrees of this complex number
A LaTex expression showing -6 - 6i
a A LaTex expression showing (4, 360 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 (6.3, 198 to the power of \ circ)
e A LaTex expression showing (4.1, 194 to the power of \ circ)
f A LaTex expression showing (8.5, 225 to the power of \ circ)
5
Find the modulus and argument (r, θ) in degrees of this complex number
A LaTex expression showing -3 - 4i
a A LaTex expression showing (4.1, 104 to the power of \ circ)
b A LaTex expression showing (5, 233 to the power of \ circ)
c A LaTex expression showing (2, 270 to the power of \ circ)
d A LaTex expression showing (3.2, 72 to the power of \ circ)
e A LaTex expression showing (1.4, 135 to the power of \ circ)
f A LaTex expression showing (2.2, 243 to the power of \ circ)
6
Find the modulus and argument (r, θ) in degrees of this complex number
A LaTex expression showing 5 + 2i
a A LaTex expression showing (7.1, 8 to the power of \ circ)
b A LaTex expression showing (7.6, 23 to the power of \ circ)
c A LaTex expression showing (6.1, 9 to the power of \ circ)
d A LaTex expression showing (9.1, 354 to the power of \ circ)
e A LaTex expression showing (9.1, 6 to the power of \ circ)
f A LaTex expression showing (5.4, 22 to the power of \ circ)
7
Find the modulus and argument (r, θ) in degrees of this complex number
A LaTex expression showing 2 + 2i
a A LaTex expression showing (3.6, 34 to the power of \ circ)
b A LaTex expression showing (5, 307 to the power of \ circ)
c A LaTex expression showing (3.6, 56 to the power of \ circ)
d A LaTex expression showing (5.7, 315 to the power of \ circ)
e A LaTex expression showing (7.2, 236 to the power of \ circ)
f A LaTex expression showing (2.8, 45 to the power of \ circ)