Complex Numbers - Rectangular Form to Modulus and Argument (Degrees) (Level 1) - Mobius Math

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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Rectangular Form to Modulus and Argument (Degrees)

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

Find the modulus and argument (r, θ) in degrees of this complex number

5 + 2i

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

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/

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 $A LaTex expression showing (8.5, 225 to the power of \ circ)$

c $A LaTex expression showing (6.3, 198 to the power of \ circ)$

d $A LaTex expression showing (5.7, 225 to the power of \ circ)$

e $A LaTex expression showing (5.7, 135 to the power of \ circ)$

f $A LaTex expression showing (4.1, 194 to the power of \ circ)$

Find the modulus and argument (r, θ) in degrees of this complex number

A LaTex expression showing -6 + 4i

a $A LaTex expression showing (7.2, 146 to the power of \ circ)$

b $A LaTex expression showing (6.4, 39 to the power of \ circ)$

c $A LaTex expression showing (4.2, 45 to the power of \ circ)$

d $A LaTex expression showing (6.3, 198 to the power of \ circ)$

e $A LaTex expression showing (5.4, 22 to the power of \ circ)$

f $A LaTex expression showing (6.1, 171 to the power of \ circ)$

Find the modulus and argument (r, θ) in degrees of this complex number

A LaTex expression showing 5 - 6i

a $A LaTex expression showing (10, 307 to the power of \ circ)$

b $A LaTex expression showing (6.7, 63 to the power of \ circ)$

c $A LaTex expression showing (4, 270 to the power of \ circ)$

d $A LaTex expression showing (7.8, 310 to the power of \ circ)$

e $A LaTex expression showing (6.1, 99 to the power of \ circ)$

f $A LaTex expression showing (2, 270 to the power of \ circ)$

Find the modulus and argument (r, θ) in degrees of this complex number

A LaTex expression showing 3 + 2i

a $A LaTex expression showing (3, 360 to the power of \ circ)$

b $A LaTex expression showing (2.2, 27 to the power of \ circ)$

c $A LaTex expression showing (3.6, 304 to the power of \ circ)$

d $A LaTex expression showing (3.6, 34 to the power of \ circ)$

e $A LaTex expression showing (4.2, 315 to the power of \ circ)$

f $A LaTex expression showing (2.8, 315 to the power of \ circ)$

Find the modulus and argument (r, θ) in degrees of this complex number

A LaTex expression showing -5 + 5i

a $A LaTex expression showing (5.1, 169 to the power of \ circ)$

b $A LaTex expression showing (5, 360 to the power of \ circ)$

c $A LaTex expression showing (7, 360 to the power of \ circ)$

d $A LaTex expression showing (7.1, 135 to the power of \ circ)$

e $A LaTex expression showing (6.4, 141 to the power of \ circ)$

f $A LaTex expression showing (6.1, 171 to the power of \ circ)$

Find the modulus and argument (r, θ) in degrees of this complex number

A LaTex expression showing 4 - 3i

a $A LaTex expression showing (5, 217 to the power of \ circ)$

b $A LaTex expression showing (5.4, 338 to the power of \ circ)$

c $A LaTex expression showing (5, 323 to the power of \ circ)$

d $A LaTex expression showing (8.6, 216 to the power of \ circ)$

e $A LaTex expression showing (7.8, 220 to the power of \ circ)$

f $A LaTex expression showing (5.7, 315 to the power of \ circ)$

Find the modulus and argument (r, θ) in degrees of this complex number

A LaTex expression showing -5 - 6i

a $A LaTex expression showing (5.4, 292 to the power of \ circ)$

b $A LaTex expression showing (4, 270 to the power of \ circ)$

c $A LaTex expression showing (6.7, 207 to the power of \ circ)$

d $A LaTex expression showing (5, 233 to the power of \ circ)$

e $A LaTex expression showing (7.8, 230 to the power of \ circ)$

f $A LaTex expression showing (5, 323 to the power of \ circ)$