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If z = 1 + i√3, find |z|^2.
If z = 1 + i√3, find |z|^2.
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Practice Questions
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Q1
If z = 1 + i√3, find |z|^2.
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|z|^2 = (1)^2 + (√3)^2 = 1 + 3 = 4.
Questions & Step-by-step Solutions
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Q: If z = 1 + i√3, find |z|^2.
Solution:
|z|^2 = (1)^2 + (√3)^2 = 1 + 3 = 4.
Steps: 7
Show Steps
Step 1: Identify the complex number z, which is given as z = 1 + i√3.
Step 2: Recall the formula for the magnitude squared of a complex number z = a + bi, which is |z|^2 = a^2 + b^2.
Step 3: In our case, a = 1 and b = √3.
Step 4: Calculate a^2, which is (1)^2 = 1.
Step 5: Calculate b^2, which is (√3)^2 = 3.
Step 6: Add the results from Step 4 and Step 5: 1 + 3 = 4.
Step 7: Conclude that |z|^2 = 4.
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