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Complex Number

Rectangular to Exponential Form (Radians) (Level 1)

This math topic focuses on converting complex numbers from rectangular form to exponential form using radians. Students practice finding the correct exponential form of various complex numbers, expressed in the format with a modulus and an exponentiated imaginary unit with a radian angle. Each question includes a complex number and multiple choice answers with different exponential forms, where students need to select the correct transformation. This exercise is part of a broader unit dedicated to complex numbers.

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

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Rectangular to Exponential Form (Radians)

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

Find the exponential form in radians of this complex number

4+5i4 + 5i

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Complex Numbers - Rectangular to Exponential Form (Radians) Worksheet

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Math worksheet on 'Complex Numbers - Rectangular to Exponential Form (Radians) (Level 1)'. Part of a broader unit on 'Complex Numbers' Learn online: app.mobius.academy/math/units/complex_numbers/
1
Find the exponential form in radians of this complex number
A LaTex expression showing 4 + 5i
a A LaTex expression showing 9.5e to the power of 1.4 Pi i
b A LaTex expression showing 8.5e to the power of 17 over 18 Pi i
c A LaTex expression showing 7.2e to the power of 1.3 Pi i
d A LaTex expression showing 7.6e to the power of 0.4 Pi i
e A LaTex expression showing 6.7e to the power of 1.4 Pi i
f A LaTex expression showing 6.4e to the power of 0.3 Pi i
2
Find the exponential form in radians of this complex number
A LaTex expression showing 2 - 6i
a A LaTex expression showing 6.4e to the power of 1.7 Pi i
b A LaTex expression showing 5.1e to the power of 1.6 Pi i
c A LaTex expression showing 7.6e to the power of 0.4 Pi i
d A LaTex expression showing 6e to the power of 11 over 2 Pi i
e A LaTex expression showing 7.3e to the power of 1.6 Pi i
f A LaTex expression showing 6.3e to the power of 1.6 Pi i
3
Find the exponential form in radians of this complex number
A LaTex expression showing -4 + 3i
a A LaTex expression showing 7.2e to the power of 1.2 Pi i
b A LaTex expression showing 9.8e to the power of 1.1 Pi i
c A LaTex expression showing 7.6e to the power of 1.1 Pi i
d A LaTex expression showing 4.2e to the power of 1.3 Pi i
e A LaTex expression showing 8.5e to the power of 11 over 9 Pi i
f A LaTex expression showing 5e to the power of 0.8 Pi i
4
Find the exponential form in radians of this complex number
A LaTex expression showing -4 + 4i
a A LaTex expression showing 5.7e to the power of 0.8 Pi i
b A LaTex expression showing 8.2e to the power of 1.4 Pi i
c A LaTex expression showing 4.5e to the power of 1.4 Pi i
d A LaTex expression showing 4.1e to the power of 0.9 Pi i
e A LaTex expression showing 5.4e to the power of 0.9 Pi i
f A LaTex expression showing 4.2e to the power of 0.8 Pi i
5
Find the exponential form in radians of this complex number
A LaTex expression showing 4 - 6i
a A LaTex expression showing 7.3e to the power of 1.6 Pi i
b A LaTex expression showing 2.2e to the power of 0.9 Pi i
c A LaTex expression showing 7.2e to the power of 1.7 Pi i
d A LaTex expression showing 4.5e to the power of 0.6 Pi i
e A LaTex expression showing 3.2e to the power of 0.9 Pi i
f A LaTex expression showing 8.2e to the power of 0.6 Pi i
6
Find the exponential form in radians of this complex number
A LaTex expression showing 3 - 5i
a A LaTex expression showing 5e to the power of 1.8 Pi i
b A LaTex expression showing 6.4e to the power of 1.8 Pi i
c A LaTex expression showing 5.7e to the power of 0.8 Pi i
d A LaTex expression showing 3.6e to the power of 1.8 Pi i
e A LaTex expression showing 5.4e to the power of 1.9 Pi i
f A LaTex expression showing 5.8e to the power of 1.7 Pi i
7
Find the exponential form in radians of this complex number
A LaTex expression showing -5 + 5i
a A LaTex expression showing 5.1e to the power of 0.9 Pi i
b A LaTex expression showing 7.1e to the power of 0.8 Pi i
c A LaTex expression showing 4.1e to the power of 0.1 Pi i
d A LaTex expression showing 5e to the power of 2 Pi i
e A LaTex expression showing 5.7e to the power of 0.8 Pi i
f A LaTex expression showing 3.6e to the power of 0.8 Pi i