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Complex Numbers

Rectangular Form to Polar Form (Radians) (Level 1)

This math topic focuses on converting complex numbers from rectangular form to polar form using radians. Each question provides a complex number in rectangular form and multiple choices for the polar form equivalent, expressed with trigonometric functions (cosine and sine). The skill practiced involves understanding complex number representations and manipulating trigonometric identities, with the objective of reinforcing the concept and calculation of polar forms in 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 Polar Form (Radians) Worksheet

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Math worksheet on 'Complex Numbers - Rectangular Form to Polar Form (Radians) (Level 1)'. Part of a broader unit on 'Complex Numbers' Learn online: app.mobius.academy/math/units/complex_numbers/
1
Find the polar form in radians of this complex number
A LaTex expression showing 5 - 5i
a A LaTex expression showing 8.7(cos(1.8 Pi \;rad) + i times sin(1.8 Pi \;rad))
b A LaTex expression showing 9.7(cos(0.1 Pi \;rad) + i times sin(0.1 Pi \;rad))
c A LaTex expression showing 8.1(cos(12 over 3 Pi \;rad) + i times sin(12 over 3 Pi \;rad))
d A LaTex expression showing 7.1(cos(1.9 Pi \;rad) + i times sin(1.9 Pi \;rad))
e A LaTex expression showing 9.7(cos(1.8 Pi \;rad) + i times sin(1.8 Pi \;rad))
f A LaTex expression showing 7.1(cos(1.8 Pi \;rad) + i times sin(1.8 Pi \;rad))
2
Find the polar form in radians of this complex number
A LaTex expression showing -6 - 3i
a A LaTex expression showing 6.1(cos(117 over 18 Pi \;rad) + i times sin(117 over 18 Pi \;rad))
b A LaTex expression showing 5.3(cos(0.1 Pi \;rad) + i times sin(0.1 Pi \;rad))
c A LaTex expression showing 6.1(cos(2 Pi \;rad) + i times sin(2 Pi \;rad))
d A LaTex expression showing 6.1(cos(1.9 Pi \;rad) + i times sin(1.9 Pi \;rad))
e A LaTex expression showing 6.7(cos(1.1 Pi \;rad) + i times sin(1.1 Pi \;rad))
f A LaTex expression showing 6.3(cos(2 Pi \;rad) + i times sin(2 Pi \;rad))
3
Find the polar form in radians of this complex number
A LaTex expression showing 3 - 4i
a A LaTex expression showing 10.1(cos(1.8 Pi \;rad) + i times sin(1.8 Pi \;rad))
b A LaTex expression showing 9(cos(1.7 Pi \;rad) + i times sin(1.7 Pi \;rad))
c A LaTex expression showing 4.2(cos(111 over 18 Pi \;rad) + i times sin(111 over 18 Pi \;rad))
d A LaTex expression showing 6.4(cos(1.6 Pi \;rad) + i times sin(1.6 Pi \;rad))
e A LaTex expression showing 5(cos(1.7 Pi \;rad) + i times sin(1.7 Pi \;rad))
f A LaTex expression showing 7.7(cos(1.6 Pi \;rad) + i times sin(1.6 Pi \;rad))
4
Find the polar form in radians of this complex number
A LaTex expression showing 2 + 3i
a A LaTex expression showing 3.6(cos(0.3 Pi \;rad) + i times sin(0.3 Pi \;rad))
b A LaTex expression showing 6.3(cos(0.3 Pi \;rad) + i times sin(0.3 Pi \;rad))
c A LaTex expression showing 6.5(cos(5 over 18 Pi \;rad) + i times sin(5 over 18 Pi \;rad))
d A LaTex expression showing 7(cos(0.3 Pi \;rad) + i times sin(0.3 Pi \;rad))
e A LaTex expression showing 3.2(cos(0.4 Pi \;rad) + i times sin(0.4 Pi \;rad))
f A LaTex expression showing 3.2(cos(1.4 Pi \;rad) + i times sin(1.4 Pi \;rad))
5
Find the polar form in radians of this complex number
A LaTex expression showing 4 + 2i
a A LaTex expression showing 4.5(cos(0.1 Pi \;rad) + i times sin(0.1 Pi \;rad))
b A LaTex expression showing 5.7(cos(0.2 Pi \;rad) + i times sin(0.2 Pi \;rad))
c A LaTex expression showing 6.3(cos(2 over 9 Pi \;rad) + i times sin(2 over 9 Pi \;rad))
d A LaTex expression showing 7.1(cos(0.3 Pi \;rad) + i times sin(0.3 Pi \;rad))
e A LaTex expression showing 7.9(cos(0.1 Pi \;rad) + i times sin(0.1 Pi \;rad))
f A LaTex expression showing 5.8(cos(1 over 3 Pi \;rad) + i times sin(1 over 3 Pi \;rad))
6
Find the polar form in radians of this complex number
A LaTex expression showing -4 + 2i
a A LaTex expression showing 4.5(cos(0.9 Pi \;rad) + i times sin(0.9 Pi \;rad))
b A LaTex expression showing 6.6(cos(1.8 Pi \;rad) + i times sin(1.8 Pi \;rad))
c A LaTex expression showing 4.9(cos(0.3 Pi \;rad) + i times sin(0.3 Pi \;rad))
d A LaTex expression showing 5.8(cos(1.8 Pi \;rad) + i times sin(1.8 Pi \;rad))
e A LaTex expression showing 5.1(cos(1.6 Pi \;rad) + i times sin(1.6 Pi \;rad))
f A LaTex expression showing 5.1(cos(1.7 Pi \;rad) + i times sin(1.7 Pi \;rad))
7
Find the polar form in radians of this complex number
A LaTex expression showing 5 - 4i
a A LaTex expression showing 3.6(cos(1.9 Pi \;rad) + i times sin(1.9 Pi \;rad))
b A LaTex expression showing 6.4(cos(1.8 Pi \;rad) + i times sin(1.8 Pi \;rad))
c A LaTex expression showing 4.7(cos(17 over 9 Pi \;rad) + i times sin(17 over 9 Pi \;rad))
d A LaTex expression showing 3.8(cos(1.7 Pi \;rad) + i times sin(1.7 Pi \;rad))
e A LaTex expression showing 5.8(cos(18 over 9 Pi \;rad) + i times sin(18 over 9 Pi \;rad))
f A LaTex expression showing 1.8(cos(0.2 Pi \;rad) + i times sin(0.2 Pi \;rad))