Complex Numbers - Polar to Exponential Form (Radians) (Level 1) - Mobius Math Academy

Complex Numbers

Polar to Exponential Form (Radians) (Level 1)

This math topic focuses on converting complex numbers from polar form to exponential form using radians. It includes multiple problems where students must calculate the exponential form of given complex numbers, represented in the format involving both cosine and sine functions of angles in radians. Each problem provides a trigonometric expression of a complex number and various options for its exponential counterpart, aiding in the understanding of the relationship between polar and exponential representations of complex numbers in the context of Euler's formula.

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

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Complex Numbers - Polar to Exponential Form (Radians) Worksheet

Complex Numbers - Polar to Exponential Form (Radians)

$A LaTex expression showing 4.2(cos(0.3 Pi \;rad) + i times sin(0.3 Pi \;rad))$

Find the exponential form in radians of this complex number

A LaTex expression showing 4.2e to the power of 0.3 Pi i

A LaTex expression showing 5e to the power of 0.3 Pi i

A LaTex expression showing 6.7e to the power of 1.4 Pi i

A LaTex expression showing 4.5e to the power of 1.4 Pi i

A LaTex expression showing 5.4e to the power of 0.4 Pi i

A LaTex expression showing 6.4e to the power of 1.3 Pi i

$A LaTex expression showing 4.5(cos(0.9 Pi \;rad) + i times sin(0.9 Pi \;rad))$

Find the exponential form in radians of this complex number

A LaTex expression showing 4.1e to the power of 0.4 Pi i

A LaTex expression showing 5e to the power of 2 Pi i

A LaTex expression showing 2.2e to the power of 1.6 Pi i

A LaTex expression showing 4.5e to the power of 0.9 Pi i

A LaTex expression showing 2.2e to the power of 1.4 Pi i

A LaTex expression showing 3e to the power of 2 Pi i

$A LaTex expression showing 5.8(cos(0.7 Pi \;rad) + i times sin(0.7 Pi \;rad))$

Find the exponential form in radians of this complex number

A LaTex expression showing 7.1e to the power of 0.5 Pi i

A LaTex expression showing 9.5e to the power of 0.4 Pi i

A LaTex expression showing 6.7e to the power of 0.4 Pi i

A LaTex expression showing 5.7e to the power of 0.3 Pi i

A LaTex expression showing 5.8e to the power of 0.7 Pi i

A LaTex expression showing 10.4e to the power of 0.4 Pi i

$A LaTex expression showing 6.4(cos(0.8 Pi \;rad) + i times sin(0.8 Pi \;rad))$

Find the exponential form in radians of this complex number

A LaTex expression showing 4e to the power of 11 over 2 Pi i

A LaTex expression showing 6.4e to the power of 0.8 Pi i

A LaTex expression showing 3.2e to the power of 1.6 Pi i

A LaTex expression showing 3.6e to the power of 0.7 Pi i

A LaTex expression showing 2e to the power of 11 over 2 Pi i

A LaTex expression showing 4.5e to the power of 0.9 Pi i

$A LaTex expression showing 7.2(cos(1.7 Pi \;rad) + i times sin(1.7 Pi \;rad))$

Find the exponential form in radians of this complex number

A LaTex expression showing 8.2e to the power of 0.1 Pi i

A LaTex expression showing 7.2e to the power of 0.2 Pi i

A LaTex expression showing 8.5e to the power of 0.3 Pi i

A LaTex expression showing 8.1e to the power of 0 Pi i

A LaTex expression showing 8.9e to the power of 0.1 Pi i

A LaTex expression showing 7.2e to the power of 1.7 Pi i

$A LaTex expression showing 5.8(cos(1.8 Pi \;rad) + i times sin(1.8 Pi \;rad))$

Find the exponential form in radians of this complex number

A LaTex expression showing 5.8e to the power of 1.8 Pi i

A LaTex expression showing 10.8e to the power of 1.1 Pi i

A LaTex expression showing 5.4e to the power of 0.1 Pi i

A LaTex expression showing 7.2e to the power of 1.2 Pi i

A LaTex expression showing 8.9e to the power of 1.9 Pi i

A LaTex expression showing 5.4e to the power of 1.1 Pi i

$A LaTex expression showing 6.3(cos(0.9 Pi \;rad) + i times sin(0.9 Pi \;rad))$

Find the exponential form in radians of this complex number

A LaTex expression showing 6.1e to the power of 17 over 18 Pi i

A LaTex expression showing 8.6e to the power of 1.8 Pi i

A LaTex expression showing 9.2e to the power of 1.8 Pi i

A LaTex expression showing 6.7e to the power of 1.9 Pi i

A LaTex expression showing 7.2e to the power of 0.8 Pi i

A LaTex expression showing 6.3e to the power of 0.9 Pi i

$A LaTex expression showing 5.7(cos(0.3 Pi \;rad) + i times sin(0.3 Pi \;rad))$

Find the exponential form in radians of this complex number

A LaTex expression showing 3.2e to the power of 1.1 Pi i

A LaTex expression showing 5.1e to the power of 1.4 Pi i

A LaTex expression showing 5.7e to the power of 0.3 Pi i

A LaTex expression showing 5.4e to the power of 1.1 Pi i

A LaTex expression showing 2.2e to the power of 1.4 Pi i

A LaTex expression showing 3.6e to the power of 0.2 Pi i