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Complex Numbers

Exponential to Polar Form (Radians) (Level 1)

This math topic focuses on converting complex numbers from exponential form to polar form, specifically using radians. It delves into understanding and applying the Euler's formula and manipulating expressions involving trigonometric functions like cosine and sine, combined with complex numbers. The questions guide learners on finding the polar form by interpreting the modulus and argument of complex numbers presented in exponential form. This exercise enhances understanding of complex numbers' properties and their representation in different forms, essential for higher mathematics, physics, and engineering studies.

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

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Complex Numbers - Exponential to Polar Form (Radians) Worksheet

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Math worksheet on 'Complex Numbers - Exponential 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 that is in exponential form
A LaTex expression showing 5.8e to the power of 0.7 Pi i
a A LaTex expression showing 3.9(cos(2 Pi \;rad) + i times sin(2 Pi \;rad))
b A LaTex expression showing 4(cos(15 over 6 Pi \;rad) + i times sin(15 over 6 Pi \;rad))
c A LaTex expression showing 5.8(cos(1 over 18 Pi \;rad) + i times sin(1 over 18 Pi \;rad))
d A LaTex expression showing 4.2(cos(0.2 Pi \;rad) + i times sin(0.2 Pi \;rad))
e A LaTex expression showing 6.2(cos(1.8 Pi \;rad) + i times sin(1.8 Pi \;rad))
f A LaTex expression showing 5.8(cos(0.7 Pi \;rad) + i times sin(0.7 Pi \;rad))
2
Find the polar form in radians of this complex number that is in exponential form
A LaTex expression showing 5e to the power of 0.3 Pi i
a A LaTex expression showing 11.7(cos(117 over 18 Pi \;rad) + i times sin(117 over 18 Pi \;rad))
b A LaTex expression showing 5(cos(0.3 Pi \;rad) + i times sin(0.3 Pi \;rad))
c A LaTex expression showing 7.6(cos(0 Pi \;rad) + i times sin(0 Pi \;rad))
d A LaTex expression showing 8.1(cos(1 over 6 Pi \;rad) + i times sin(1 over 6 Pi \;rad))
e A LaTex expression showing 13.7(cos(0 Pi \;rad) + i times sin(0 Pi \;rad))
f A LaTex expression showing 9.8(cos(0.1 Pi \;rad) + i times sin(0.1 Pi \;rad))
3
Find the polar form in radians of this complex number that is in exponential form
A LaTex expression showing 3.6e to the power of 1.7 Pi i
a A LaTex expression showing 1.9(cos(2 Pi \;rad) + i times sin(2 Pi \;rad))
b A LaTex expression showing 3.6(cos(1.7 Pi \;rad) + i times sin(1.7 Pi \;rad))
c A LaTex expression showing 2.7(cos(1.7 Pi \;rad) + i times sin(1.7 Pi \;rad))
d A LaTex expression showing 0.9(cos(2 Pi \;rad) + i times sin(2 Pi \;rad))
e A LaTex expression showing 2.8(cos(1.9 Pi \;rad) + i times sin(1.9 Pi \;rad))
f A LaTex expression showing 1.8(cos(1.8 Pi \;rad) + i times sin(1.8 Pi \;rad))
4
Find the polar form in radians of this complex number that is in exponential form
A LaTex expression showing 2.8e to the power of 0.3 Pi i
a A LaTex expression showing 3(cos(0.2 Pi \;rad) + i times sin(0.2 Pi \;rad))
b A LaTex expression showing 3.2(cos(0.1 Pi \;rad) + i times sin(0.1 Pi \;rad))
c A LaTex expression showing 5(cos(11 over 2 Pi \;rad) + i times sin(11 over 2 Pi \;rad))
d A LaTex expression showing 2.8(cos(0.3 Pi \;rad) + i times sin(0.3 Pi \;rad))
e A LaTex expression showing 3(cos(11 over 2 Pi \;rad) + i times sin(11 over 2 Pi \;rad))
f A LaTex expression showing 2(cos(2 Pi \;rad) + i times sin(2 Pi \;rad))
5
Find the polar form in radians of this complex number that is in exponential form
A LaTex expression showing 5.7e to the power of 0.8 Pi i
a A LaTex expression showing 5.7(cos(0.8 Pi \;rad) + i times sin(0.8 Pi \;rad))
b A LaTex expression showing 6.4(cos(0.3 Pi \;rad) + i times sin(0.3 Pi \;rad))
c A LaTex expression showing 7(cos(0.5 Pi \;rad) + i times sin(0.5 Pi \;rad))
d A LaTex expression showing 11.7(cos(0.3 Pi \;rad) + i times sin(0.3 Pi \;rad))
e A LaTex expression showing 7.8(cos(5 over 18 Pi \;rad) + i times sin(5 over 18 Pi \;rad))
f A LaTex expression showing 8.3(cos(0.3 Pi \;rad) + i times sin(0.3 Pi \;rad))
6
Find the polar form in radians of this complex number that is in exponential form
A LaTex expression showing 5.4e to the power of 0.9 Pi i
a A LaTex expression showing 6.1(cos(0.3 Pi \;rad) + i times sin(0.3 Pi \;rad))
b A LaTex expression showing 7.8(cos(1.6 Pi \;rad) + i times sin(1.6 Pi \;rad))
c A LaTex expression showing 10.3(cos(1.6 Pi \;rad) + i times sin(1.6 Pi \;rad))
d A LaTex expression showing 6.3(cos(0.2 Pi \;rad) + i times sin(0.2 Pi \;rad))
e A LaTex expression showing 4.1(cos(0.4 Pi \;rad) + i times sin(0.4 Pi \;rad))
f A LaTex expression showing 5.4(cos(0.9 Pi \;rad) + i times sin(0.9 Pi \;rad))
7
Find the polar form in radians of this complex number that is in exponential form
A LaTex expression showing 7.1e to the power of 1.8 Pi i
a A LaTex expression showing 10.1(cos(1.9 Pi \;rad) + i times sin(1.9 Pi \;rad))
b A LaTex expression showing 8.1(cos(2 Pi \;rad) + i times sin(2 Pi \;rad))
c A LaTex expression showing 12.3(cos(0.1 Pi \;rad) + i times sin(0.1 Pi \;rad))
d A LaTex expression showing 8.6(cos(18 over 9 Pi \;rad) + i times sin(18 over 9 Pi \;rad))
e A LaTex expression showing 11.3(cos(1.9 Pi \;rad) + i times sin(1.9 Pi \;rad))
f A LaTex expression showing 7.1(cos(1.8 Pi \;rad) + i times sin(1.8 Pi \;rad))