Question Detail

MTH 101 MTH 101 Past Questions Objective Question
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Question

Let z = x + iy where x and y are real numbers and y ≠ 0. Compute the value of log(2+3i).
Options
A log 13 + i tan⁻¹(3/2)
B log 13 - i tan⁻¹(3/2)
C log √13 + i tan⁻¹(3/2)
Correct Answer
D log √13 - i tan⁻¹(3/2)
Correct Answer

Option C is the correct answer.

Detailed Explanation

For a complex number z = a + ib, log z = ln|z| + i arg(z). |2+3i| = √(2²+3²) = √13, arg(2+3i) = tan⁻¹(3/2). So log(2+3i) = ln(√13) + i tan⁻¹(3/2).

Hint

Use the formula log(z) = ln|z| + i arg(z).

Question Info

Course: MTH 101
Topic: MTH 101 Past Questions
Type: Objective
Difficulty: Not specified
Question 401 of 696
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