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If z = re^(iθ), what is the value of z^2?
If z = re^(iθ), what is the value of z^2?
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Practice Questions
1 question
Q1
If z = re^(iθ), what is the value of z^2?
r^2e^(i2θ)
re^(iθ)
2re^(iθ)
r^2e^(iθ)
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Using the property of exponents, z^2 = (re^(iθ))^2 = r^2e^(i2θ).
Questions & Step-by-step Solutions
1 item
Q
Q: If z = re^(iθ), what is the value of z^2?
Solution:
Using the property of exponents, z^2 = (re^(iθ))^2 = r^2e^(i2θ).
Steps: 8
Show Steps
Step 1: Start with the given expression for z, which is z = re^(iθ).
Step 2: To find z^2, we need to square the expression for z.
Step 3: Write z^2 as (re^(iθ))^2.
Step 4: Use the property of exponents that states (a*b)^n = a^n * b^n.
Step 5: Apply this property: (re^(iθ))^2 = r^2 * (e^(iθ))^2.
Step 6: Now, square e^(iθ) using the property (e^(iθ))^2 = e^(i*2θ).
Step 7: Combine the results: z^2 = r^2 * e^(i*2θ).
Step 8: Write the final result as z^2 = r^2e^(i2θ).
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