If z = 1 + i√3, find the modulus of z.

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Question: If z = 1 + i√3, find the modulus of z.

Options:

Correct Answer: 2

Solution:

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

If z = 1 + i√3, find the modulus of z.

If z = 1 + i√3, find the modulus of z.

Correct Answer: 2

Step 1: Identify the complex number z, which is given as z = 1 + i√3.
Step 2: Recognize that the modulus 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: 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: Take the square root of the sum from Step 6: √4 = 2.
Step 8: Conclude that the modulus of z is |z| = 2.

Complex Numbers – Understanding the representation of complex numbers in the form a + bi, where a is the real part and b is the imaginary part.
Modulus of a Complex Number – The modulus of a complex number z = a + bi is calculated using the formula |z| = √(a^2 + b^2).