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The Argand diagram shows the complex numbers z and w, where z lies in the first quadrant and w lies in the second quadrant - HSC - SSCE Mathematics Extension 2 - Question 4 - 2016 - Paper 1
Question 4
The Argand diagram shows the complex numbers z and w, where z lies in the first quadrant and w lies in the second quadrant. Which complex number could lie in the 3r... show full transcript
Worked Solution & Example Answer:The Argand diagram shows the complex numbers z and w, where z lies in the first quadrant and w lies in the second quadrant - HSC - SSCE Mathematics Extension 2 - Question 4 - 2016 - Paper 1
Step 1
−w
Answer
The complex number −w will lie in the third quadrant because w lies in the second quadrant. In the Argand diagram, the second quadrant has a negative real part and a positive imaginary part. When we negate w, we convert this into a positive real part and a negative imaginary part, thereby placing −w in the third quadrant.
Step 2
Step 3
Step 4
w − z
Answer
The expression w - z will yield a complex number that could potentially lie in various quadrants depending on the values of w and z. However, since both numbers have positive components affecting real and imaginary parts, it is unfitting to conclude that this will always lie in the third quadrant.