In which quadrant is the complex number $6-8i$ located on the complex plane?

• A. Quadrant IV
• B. Quadrant II
• C. Quadrant I
• D. Quadrant III

Answer: (A)

Verified step by step guidance

1. Recall that a complex number is represented on the complex plane as a point with coordinates \((x, y)\), where \(x\) is the real part and \(y\) is the imaginary part.
2. Identify the real and imaginary parts of the complex number \$6 - 8i\(. Here, the real part is \)6\( and the imaginary part is \)-8$.
3. Plot the point \((6, -8)\) on the complex plane. The \(x\)-coordinate is positive (6), and the \(y\)-coordinate is negative (-8).
4. Determine the quadrant based on the signs of \(x\) and \(y\): - Quadrant I: \(x > 0\), \(y > 0\) - Quadrant II: \(x < 0\), \(y > 0\) - Quadrant III: \(x < 0\), \(y < 0\) - Quadrant IV: \(x > 0\), \(y < 0\)
5. Since \(x\) is positive and \(y\) is negative, the point lies in Quadrant IV.