Answer:
Z = 5 + 3i and Z = -8 - 2i
Step-by-step explanation:
* Lets study the drawing of the complex numbers
- The x-axis is the real axis
- The y-axis is the imaginary axis
* Look to the attached figure
- Any point in the first quadrant is above the real axis and right
to the imaginary axis (Z4)
# Z = x + yi
- Any point in the second quadrant is above the real axis and left
to the imaginary axis (Z2)
# Z = -x + yi
- Any point in the third quadrant is below the real axis and left
to the imaginary axis (Z3)
# Z = -x - yi
- Any point in the fourth quadrant is below the real axis and right
to the imaginary axis (Z1)
# Z = x - yi
* Now lets solve the problem
- The point above the real axis and right to the imaginary axis lies
in the first quadrant
∴ The real part is positive and the imaginary part is positive
∴ Z = 5 + 3i
- The point below the real axis and left to the imaginary axis lies
in the third quadrant
∴ The real part is negative and the imaginary part is negative
∴ Z = -8 - 2i
