What is the square root of the complex number -4? (2020)

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Question: What is the square root of the complex number -4? (2020)

Options:

Correct Answer: 2i

Exam Year: 2020

Solution:

The square root of -4 is √(-1) * √4 = 2i.

What is the square root of the complex number -4? (2020)

What is the square root of the complex number -4? (2020)

Step 1: Recognize that -4 can be expressed as -1 times 4, so we write -4 = -1 * 4.
Step 2: Use the property of square roots that says √(a * b) = √a * √b. Here, we apply it to -4: √(-4) = √(-1 * 4) = √(-1) * √(4).
Step 3: Calculate the square root of 4, which is 2, so we have √(4) = 2.
Step 4: Recognize that the square root of -1 is represented by the imaginary unit 'i', so √(-1) = i.
Step 5: Combine the results from Step 3 and Step 4: √(-4) = i * 2 = 2i.

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