The diagram shows the complex number $z$ on the Argand diagram - HSC - SSCE Mathematics Extension 2 - Question 4 - 2020 - Paper 1
Question 4
The diagram shows the complex number $z$ on the Argand diagram.
Which of the following diagrams best shows the position of $ rac{-2}{|z|}$?
A.
B.
C.
D.
Worked Solution & Example Answer:The diagram shows the complex number $z$ on the Argand diagram - HSC - SSCE Mathematics Extension 2 - Question 4 - 2020 - Paper 1
Step 1
Find the modulus of z
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Answer
The modulus of a complex number z is given by ∣z∣. This is the distance from the origin to the point representing z on the Argand diagram.
Step 2
Calculate -2/|z|
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Answer
We need to evaluate the expression rac{-2}{|z|}. The result represents a complex number that lies on the real axis, at a distance of rac{2}{|z|} away from the origin, but in the negative direction.
Step 3
Identify the correct diagram
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Answer
Given that rac{-2}{|z|} is a negative real number, it will be positioned on the negative real axis on the Argand diagram. Therefore, the correct option that illustrates this position is diagram A.
