Question Detail

MTH 101 MTH 101 Past Questions Objective Question
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Question

Express \(\frac{2+5i}{i} + \frac{2}{4-i}\) in the rectangular form a + ib.
Options
A \(\frac{22}{17} + \frac{37}{17}i\)
Correct Answer
B \(\frac{22}{17} - \frac{37}{17}i\)
C \(\frac{22}{17} + \frac{37}{17}i\)
D \(\frac{4}{17} - \frac{37}{17}i\)
Correct Answer

Option A is the correct answer.

Detailed Explanation

First term: (2+5i)/i = (2+5i)(-i)/1 = -2i -5i² = -2i +5 = 5 - 2i. Second term: 2/(4-i) = 2(4+i)/(16+1) = (8+2i)/17 = 8/17 + (2/17)i. Sum: (5 + 8/17) + (-2 + 2/17)i = (85/17+8/17) + (-34/17+2/17)i = (93/17) - (32/17)i. Not matching options. Option A is 22/17 + 37/17i. There may be a misprint.

Hint

Multiply numerator and denominator by the conjugate to simplify.

Question Info

Course: MTH 101
Topic: MTH 101 Past Questions
Type: Objective
Difficulty: Not specified
Question 665 of 696
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