What is the square of the modulus of the complex number 1 + 2i? (2014)

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Question: What is the square of the modulus of the complex number 1 + 2i? (2014)

Options:

Correct Answer: 5

Solution:

The modulus is √(1^2 + 2^2) = √(1 + 4) = √5. The square of the modulus is 5.

What is the square of the modulus of the complex number 1 + 2i? (2014)

What is the square of the modulus of the complex number 1 + 2i? (2014)

Step 1: Identify the complex number. The complex number given is 1 + 2i.
Step 2: Write down the formula for the modulus of a complex number. The modulus is calculated using the formula √(a^2 + b^2), where a is the real part and b is the imaginary part.
Step 3: Identify the real part and the imaginary part. Here, a = 1 and b = 2.
Step 4: Substitute the values of a and b into the modulus formula. This gives us √(1^2 + 2^2).
Step 5: Calculate 1^2 and 2^2. We find that 1^2 = 1 and 2^2 = 4.
Step 6: Add the results from Step 5. So, 1 + 4 = 5.
Step 7: Take the square root of the sum from Step 6. This gives us √5.
Step 8: Now, find the square of the modulus. The square of √5 is (√5)^2, which equals 5.

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