Question

Hello! Would like help on parts a & b. Thanks!

Answer 1

Part A

Looking at the graph

we have that

z1 ------> the coordinates are (3,5)

so

the standard form is z1=3+5i

z2 ------> the coordinates are (6,-3)

so

the standard form is z2=6-3i

Find out the distance between them

z2-z1=(6-3i)-(3+5i)

z2-z1=(6-3)+(-3i-5i)

z2-z1=3-8i

Find out the magnitude of the complex number (Applying the Pythagorean Theorem)

$\begin{gathered} d_{z1z2}=\sqrt{(3)^2+(-8)^2} \\ d_{z1z2}=\sqrt{73} \end{gathered}$

The distance between z1 and z2 is the square root of 73 units

Part B

Find out the conjugate of z2

we have

z2=6-3i

so

Remember that

You find the complex conjugate simply by changing the sign of the imaginary part of the complex number

therefore

The conjugate of z2 is (6+3i)

To find out geometrically change the sign of the y-coordinate (imaginary part) of the complex number (Reflect the given point over the x-axis)