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Algebra Difficulty 2.9 Junior Find the answer

In the complex plane, the point corresponding to the complex number 23ii\frac{-2-3i}{i} is located in

Pick one

Solutions — 2

Solution 1

Analysis

We will simplify the complex number by using the algebraic form of complex number multiplication and division to find the coordinates of the point. This problem tests the basic concepts of complex numbers and their multiplication and division, making it a fundamental question.

Step-by-step Solution

1. Simplify the given complex number:
23ii=(23i)×1i=(23i)×(i)=2i3=3+2i\frac{-2-3i}{i} = (-2-3i) \times \frac{1}{i} = (-2-3i) \times (-i) = 2i - 3 = -3 + 2i

2. Identify the coordinates of the complex number:
The real part of the complex number is 3-3, and the imaginary part is 22. So, the coordinates of the corresponding point in the complex plane are (3,2)(-3, 2).

3. Determine the quadrant:
Since the x-coordinate is negative, and the y-coordinate is positive, the point lies in the second quadrant.

Hence, the correct answer is: B\boxed{\text{B}}.

Solution 2

Solution: The complex number 23ii\frac {-2-3i}{i} equals (23i)(i)ii\frac {(-2-3i)(-i)}{-i\cdot i} equals 2i32i-3. The corresponding point (3,2)(-3, 2) is located in the second quadrant.

Therefore, the answer is: B\boxed{\text{B}}.

This problem tests the operation rules of complex numbers and their geometric meanings, focusing on computational ability. It is a basic question.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.