Consider w sub 1 is equal to 4 plus 2 i and w sub 2 is equal to negative 1 minus 3 i Which graph represents the sum w sub 1 plus w sub 2 ?
Answer
A
Image with description A complex plane shows a horizontal axis labeled “real” and a vertical axis labeled “imaginary,” with grid lines at 1 unit intervals. A line segment extends from the origin (0 comma 0) downward to the right and ends at a filled point at (3 comma negative 5).
B
Image with description A complex plane shows a horizontal axis labeled “real” and a vertical axis labeled “imaginary,” with grid lines at 1 unit intervals. A line segment extends from the origin (0 comma 0) downward to the right and ends at a filled point at (3 comma negative 1).
C
Image with description A complex plane shows a horizontal axis labeled “real” and a vertical axis labeled “imaginary,” with grid lines at 1 unit intervals. A line segment extends from the origin (0 comma 0) upward to the right and ends at a filled point at (5 comma 5).
D
Image with description A complex plane shows a horizontal axis labeled “real” and a vertical axis labeled “imaginary,” with grid lines at 1 unit intervals. A line segment extends from the origin (0 comma 0) upward to the right and ends at a filled point at (5 comma 1).
Explanation
Add the real parts and the imaginary parts separately: (4 + 2i) + (−1 − 3i) = (4 − 1) + (2 − 3)i = 3 − i. On the complex plane, this is the point (3, −1), which is choice B.
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