What is the value of (2 + 3i) / (1 + i)? (2015)

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Question: What is the value of (2 + 3i) / (1 + i)? (2015)

Options:

1 + 2i
2 - i
3 + 2i
1 - 2i

Correct Answer: 2 - i

Solution:

Multiply numerator and denominator by the conjugate of the denominator: (2 + 3i)(1 - i) / (1 + i)(1 - i) = (2 - 2i + 3i + 3) / (1 + 1) = (5 + i) / 2 = 2.5 + 0.5i.

What is the value of (2 + 3i) / (1 + i)? (2015)

Practice Questions

What is the value of (2 + 3i) / (1 + i)? (2015)

1 + 2i
2 - i
3 + 2i
1 - 2i

Questions & Step-by-Step Solutions

What is the value of (2 + 3i) / (1 + i)? (2015)

Step 1: Identify the expression we need to simplify: (2 + 3i) / (1 + i).
Step 2: Find the conjugate of the denominator (1 + i). The conjugate is (1 - i).
Step 3: Multiply both the numerator and the denominator by the conjugate: (2 + 3i)(1 - i) / (1 + i)(1 - i).
Step 4: Calculate the denominator: (1 + i)(1 - i) = 1^2 - i^2 = 1 - (-1) = 1 + 1 = 2.
Step 5: Calculate the numerator: (2 + 3i)(1 - i) = 2*1 + 2*(-i) + 3i*1 + 3i*(-i) = 2 - 2i + 3i - 3 = (2 - 3) + (-2i + 3i) = -1 + i.
Step 6: Now we have: (-1 + i) / 2.
Step 7: Split the fraction: -1/2 + i/2 = -0.5 + 0.5i.

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What is the value of (2 + 3i) / (1 + i)? (2015)

What’s inside this PDF?

What is the value of (2 + 3i) / (1 + i)? (2015)

Practice Questions

Questions & Step-by-Step Solutions

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