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What is the value of |z|^2 if z = 4 - 3i?
What is the value of |z|^2 if z = 4 - 3i?
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Practice Questions
1 question
Q1
What is the value of |z|^2 if z = 4 - 3i?
25
16
7
12
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|z|^2 = 4^2 + (-3)^2 = 16 + 9 = 25.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the value of |z|^2 if z = 4 - 3i?
Solution:
|z|^2 = 4^2 + (-3)^2 = 16 + 9 = 25.
Steps: 7
Show Steps
Step 1: Identify the complex number z. Here, z = 4 - 3i.
Step 2: Recall that the magnitude squared of a complex number z = a + bi is given by |z|^2 = a^2 + b^2.
Step 3: In our case, a = 4 and b = -3.
Step 4: Calculate a^2. This is 4^2 = 16.
Step 5: Calculate b^2. This is (-3)^2 = 9.
Step 6: Add the results from Step 4 and Step 5. So, 16 + 9 = 25.
Step 7: Conclude that |z|^2 = 25.
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