What is the square of the modulus of the complex number 1 + i? (2020)

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Question: What is the square of the modulus of the complex number 1 + i? (2020)

Options:

Correct Answer: 2

Solution:

The modulus is √(1^2 + 1^2) = √2, and the square of the modulus is 2.

What is the square of the modulus of the complex number 1 + i? (2020)

What is the square of the modulus of the complex number 1 + i? (2020)

Step 1: Identify the complex number. The complex number given is 1 + i.
Step 2: Recall the formula for the modulus of a complex number a + bi, which is √(a^2 + b^2).
Step 3: In our case, a = 1 and b = 1. So we will calculate the modulus using these values.
Step 4: Calculate a^2. Here, 1^2 = 1.
Step 5: Calculate b^2. Here, 1^2 = 1.
Step 6: Add the results from Step 4 and Step 5. So, 1 + 1 = 2.
Step 7: Take the square root of the sum from Step 6. So, √2 is the modulus.
Step 8: Now, to find the square of the modulus, we square the result from Step 7. So, (√2)^2 = 2.

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