Question: If z = 1 + i√3, find the value of |z|^2.
Options:
4
3
2
1
Correct Answer: 4
Solution:
|z|^2 = (1)^2 + (√3)^2 = 1 + 3 = 4.
If z = 1 + i√3, find the value of |z|^2.
Practice Questions
Q1
If z = 1 + i√3, find the value of |z|^2.
4
3
2
1
Questions & Step-by-Step Solutions
If z = 1 + i√3, find the value of |z|^2.
Correct Answer: 4
Step 1: Identify the complex number z. Here, 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. This is (1)^2 = 1.
Step 5: Calculate b^2. This is (√3)^2 = 3.
Step 6: Add the results from Step 4 and Step 5. This is 1 + 3 = 4.
Step 7: Conclude that |z|^2 = 4.
Complex Numbers – Understanding the representation of complex numbers in the form z = a + bi, where a is the real part and b is the imaginary part.
Magnitude of Complex Numbers – Calculating the magnitude (or modulus) of a complex number using the formula |z| = √(a^2 + b^2) and its square |z|^2 = a^2 + b^2.
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