If z = 1 + i√3, find |z|.

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Q: If z = 1 + i√3, find |z|.

Solution: |z| = √(1^2 + (√3)^2) = √(1 + 3) = √4 = 2.

Steps: 9

Step 1: Identify the complex number z, which is given as z = 1 + i√3.
Step 2: Recall that the magnitude (or absolute value) of a complex number z = a + bi is calculated using the formula |z| = √(a^2 + b^2).
Step 3: In our case, a = 1 and b = √3.
Step 4: Substitute the values of a and b into the formula: |z| = √(1^2 + (√3)^2).
Step 5: Calculate 1^2, which is 1.
Step 6: Calculate (√3)^2, which is 3.
Step 7: Add the results from Step 5 and Step 6: 1 + 3 = 4.
Step 8: Take the square root of 4: √4 = 2.
Step 9: Therefore, the magnitude |z| is 2.