Reviewed by Yaren Fadiloglulari
In which quadrant is the number 6 – 8i located on the complex plane?
Answer: 6 – 8i is located in the fourth quadrant
Complex numbers are represented on the complex plane, where the horizontal axis is the real part and the vertical axis is the imaginary part. The plane is divided into four quadrants, each corresponding to combinations of positive and negative real and imaginary parts. Identifying which quadrant a specific complex number lies in helps visualize the number's position relative to the origin.
Methods
Math Tutor Explanation Using the Signs of Real and Imaginary Parts
To determine the quadrant, check the signs of the real part (6) and the imaginary part (–8).
Step 1: The real part of 6 – 8i is 6, which is positive
Step 2: The imaginary part is –8, which is negative
Math Tutor Explanation Using Complex Plane Plotting
Visualizing where the point (6, –8) is plotted on the complex plane can help determine its quadrant.
Step 1: Plot the point where the real axis (horizontal) value is 6
Step 2: Plot the point where the imaginary axis (vertical) value is –8
Step 1:
Step 2:
Math Tutor suggests: Dive Deeper into Complex Numbers and the Coordinate Plane
If you're curious about the placement of complex numbers on the complex plane or want to expand your skills with related mathematical concepts, check out these exercises.
FAQ on Quadrants in the Complex Plane
What are the four quadrants of the complex plane?
The complex plane is divided into four quadrants based on the signs of the real and imaginary parts: I (+, +), II (–, +), III (–, –), IV (+, –).
How do you determine the quadrant of a complex number?
Check if the real and imaginary parts are positive or negative to locate the correct quadrant.
What type of numbers lie on the axes?
Points with a zero real part lie on the imaginary axis, and points with a zero imaginary part lie on the real axis.
Can a complex number be in more than one quadrant?
No, each complex number is located in exactly one quadrant unless it is on an axis.
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