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

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

This math topic focuses on converting complex numbers from rectangular form to polar form, specifically calculating the modulus and argument in radians. Each problem presents a complex number and asks to find these two components. The questions cover different values of complex numbers to practice these conversions thoroughly. Several answer choices are offered for each question, among which learners need to select the correct modulus and argument pair. The emphasis is on mastering transformations and understanding the properties of complex numbers in polar coordinates.

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 (Radians)

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

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

-5 + 3i

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

Math worksheet on 'Complex Numbers - Rectangular Form to Modulus and Argument (Radians) (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 radians of this complex number

A LaTex expression showing -6 - 6i

a $A LaTex expression showing (8.9, 1.4 Pi \;rad)$

b $A LaTex expression showing (8.5, 1.3 Pi \;rad)$

c $A LaTex expression showing (8.5, 7 over 18 Pi \;rad)$

d $A LaTex expression showing (7.8, 5 over 18 Pi \;rad)$

e $A LaTex expression showing (10, 0.7 Pi \;rad)$

f $A LaTex expression showing (7.8, 2 over 9 Pi \;rad)$

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

A LaTex expression showing 5 + 3i

a $A LaTex expression showing (7.8, 5 over 18 Pi \;rad)$

b $A LaTex expression showing (6.7, 1.6 Pi \;rad)$

c $A LaTex expression showing (7.1, 1.8 Pi \;rad)$

d $A LaTex expression showing (9.4, 1.7 Pi \;rad)$

e $A LaTex expression showing (5.8, 0.2 Pi \;rad)$

f $A LaTex expression showing (8.6, 0.3 Pi \;rad)$

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

A LaTex expression showing 2 + 4i

a $A LaTex expression showing (3.2, 0.1 Pi \;rad)$

b $A LaTex expression showing (6.3, 1.4 Pi \;rad)$

c $A LaTex expression showing (3.2, 0.9 Pi \;rad)$

d $A LaTex expression showing (3.6, 0.8 Pi \;rad)$

e $A LaTex expression showing (4.5, 0.4 Pi \;rad)$

f $A LaTex expression showing (5, 1.3 Pi \;rad)$

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

A LaTex expression showing 4 - 3i

a $A LaTex expression showing (5, 1.7 Pi \;rad)$

b $A LaTex expression showing (4.2, 1.8 Pi \;rad)$

c $A LaTex expression showing (5.8, 1.7 Pi \;rad)$

d $A LaTex expression showing (3.2, 1.9 Pi \;rad)$

e $A LaTex expression showing (4.2, 0.3 Pi \;rad)$

f $A LaTex expression showing (5, 1.8 Pi \;rad)$

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

A LaTex expression showing -6 + 3i

a $A LaTex expression showing (11.2, 0.9 Pi \;rad)$

b $A LaTex expression showing (13.4, 0.1 Pi \;rad)$

c $A LaTex expression showing (8.6, 0.8 Pi \;rad)$

d $A LaTex expression showing (13.4, 0.9 Pi \;rad)$

e $A LaTex expression showing (7.6, 0.9 Pi \;rad)$

f $A LaTex expression showing (6.7, 0.9 Pi \;rad)$

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

A LaTex expression showing 2 - 5i

a $A LaTex expression showing (5.4, 1.6 Pi \;rad)$

b $A LaTex expression showing (4.5, 0.4 Pi \;rad)$

c $A LaTex expression showing (4.5, 1.6 Pi \;rad)$

d $A LaTex expression showing (6.3, 0.4 Pi \;rad)$

e $A LaTex expression showing (6, 11 over 2 Pi \;rad)$

f $A LaTex expression showing (6.1, 5 over 9 Pi \;rad)$

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

A LaTex expression showing 4 + 5i

a $A LaTex expression showing (7.2, 0.2 Pi \;rad)$

b $A LaTex expression showing (10.8, 0.2 Pi \;rad)$

c $A LaTex expression showing (12.2, 0.2 Pi \;rad)$

d $A LaTex expression showing (6.7, 0.1 Pi \;rad)$

e $A LaTex expression showing (10, 0.2 Pi \;rad)$

f $A LaTex expression showing (6.4, 0.3 Pi \;rad)$