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

This math topic focuses on converting complex numbers from polar form (modulus and argument in radians) to rectangular form. It tests the students' ability to apply the conversion formula involving trigonometric functions like sine and cosine to determine the real and imaginary components of the complex number. Each question presents a modulus and an argument for the students to convert into a complex number in standard form, presenting multiple choices for the answers. The problems gradually increase in complexity as students progress through the questions.

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

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Modulus and Argument (Radians) to Rectangular Form

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


Find the rectangular form of the complex number that has a modulus and argument (r, θ) of

(5.4,0.9π  rad)(5.4, 0.9 \pi\;rad)

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

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Math worksheet on 'Complex Numbers - Modulus and Argument (Radians) to Rectangular Form (Level 1)'. Part of a broader unit on 'Complex Numbers' Learn online: app.mobius.academy/math/units/complex_numbers/
1
Find the rectangular form of the complex number that has a modulus and argument (r, θ) of
A LaTex expression showing (7.8, 113 over 18 Pi \;rad)
a A LaTex expression showing 3 - 6i
b A LaTex expression showing 5 - 6i
c A LaTex expression showing 1 - 8i
d A LaTex expression showing 1 - 12i
e A LaTex expression showing 1 - 10i
f A LaTex expression showing 1 - 6i
2
Find the rectangular form of the complex number that has a modulus and argument (r, θ) of
A LaTex expression showing (3.6, 0.2 Pi \;rad)
a A LaTex expression showing 2 + 3i
b A LaTex expression showing 2 + 2i
c A LaTex expression showing 2 - 3i
d A LaTex expression showing 4 + 3i
e A LaTex expression showing 3 + 3i
f A LaTex expression showing 3 + 2i
3
Find the rectangular form of the complex number that has a modulus and argument (r, θ) of
A LaTex expression showing (6.7, 1.1 Pi \;rad)
a A LaTex expression showing 6 + 1i
b A LaTex expression showing 6 + 3i
c A LaTex expression showing -6 - 3i
d A LaTex expression showing 8
e A LaTex expression showing 10
f A LaTex expression showing 6
4
Find the rectangular form of the complex number that has a modulus and argument (r, θ) of
A LaTex expression showing (5.7, 0.8 Pi \;rad)
a A LaTex expression showing -6 + 4i
b A LaTex expression showing -6 - 2i
c A LaTex expression showing -6 + 5i
d A LaTex expression showing -4 + 4i
e A LaTex expression showing -6 - 5i
f A LaTex expression showing -6 - 3i
5
Find the rectangular form of the complex number that has a modulus and argument (r, θ) of
A LaTex expression showing (4.2, 1.8 Pi \;rad)
a A LaTex expression showing 4 - 1i
b A LaTex expression showing -1i
c A LaTex expression showing 4 - 3i
d A LaTex expression showing 2 - 3i
e A LaTex expression showing 2 - 1i
f A LaTex expression showing 3 - 3i
6
Find the rectangular form of the complex number that has a modulus and argument (r, θ) of
A LaTex expression showing (5, 0.7 Pi \;rad)
a A LaTex expression showing -3 - 4i
b A LaTex expression showing -5 - 4i
c A LaTex expression showing -3 + 4i
d A LaTex expression showing -7 - 2i
e A LaTex expression showing -7 - 3i
f A LaTex expression showing -5 - 3i
7
Find the rectangular form of the complex number that has a modulus and argument (r, θ) of
A LaTex expression showing (5.4, 0.9 Pi \;rad)
a A LaTex expression showing -3
b A LaTex expression showing -3 - 2i
c A LaTex expression showing -3 - 4i
d A LaTex expression showing -5 - 2i
e A LaTex expression showing -5 + 2i
f A LaTex expression showing 3 - 4i