https://r2.erweima.ai/mathbot/image/1725533297185r3l92tpa.jpg

The image contains the following mathematical expressions:

\[
z = 2i
\]
\[
n = 6
\]

It seems that \( z \) is a complex number, purely imaginary, with \( z = 2i \), and \( n \) is given as 6. 

If you're looking for powers of this complex number \( z^n \), such as \( z^6 \), I can compute that for you or any other operation you might be interested in. Would you like to proceed with this, or do you have another question related to these expressions?

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Here are some relative questions to deepen understanding:

1. How can you calculate higher powers of a complex number?
2. What is the general form of a complex number in polar coordinates?
3. How do complex roots relate to De Moivre's theorem?
4. What is the significance of the imaginary unit \( i \) in complex numbers?
5. How would you graph the complex number \( z = 2i \) on the complex plane?

**Tip:** When raising complex numbers to powers, expressing them in polar form often simplifies calculations.

Explore how to calculate the power of a complex number, z = 2i, raised to the 6th power. This tutorial covers key concepts in complex numbers, including De Moivre's Theorem and how to handle powers of purely imaginary numbers. Suitable for students in Grades 10-12.

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