# Worksheet: Transformations of the Complex Plane

In this worksheet, we will practice translating and rotating a complex number in the complex plane.

**Q1: **

Describe the geometric transformation that occurs when numbers in the complex plane are mapped to their sum with .

- Aa translation by
- Ba translation by
- Ca translation by
- Da translation by
- Ea translation by

**Q2: **

Multiplying a complex number by corresponds to a transformation composed of a rotation by about the origin and a dilation with center at the origin and positive scale factor. What kind of number is ?

- AA positive real number
- BA negative real number
- CA positive imaginary number
- DA negative imaginary number

**Q3: **

Find an equation for the image of under the transformation of the complex plane .

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**Q4: **

Find an equation for the image of under the transformation of -plane to the -plane given by .

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**Q5: **

Given that , find an equation for under the transformation that maps the -plane onto the -plane.

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**Q6: **

Consider the complex number .

Write in exponential form.

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Find the value of .

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Find an equation for the image of under the transformation of the complex plane .

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**Q7: **

Find an equation for the image of the line under the transformation of the complex plane .

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**Q8: **

Find an equation for the image of the half line under the transformation .

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**Q9: **

Find an equation for the image of under the transformation of the complex plane , where .

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**Q10: **

In the -plane, a curve is given by the Cartesian equation . The transformation represents a transformation from the -plane to the -plane. Find the Cartesian equation for the image of the curve in the -plane.

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**Q11: **

Find an equation for the image of under the transformation of the complex plane .

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