Question

Points z1 and z2 are shown on the graph.Part A: Give the complex conjugate of z2 and explain how to find it geometrically.Part B: Find z2 − z1 geometrically and explain your steps.

Answer 1

Looking at the graph

we have that

z1=(4,6i) -------> 4+6i

z2=(-5,2i) -----> -5+2i

so

Part a

Conjugate of z2

we know that

z2=-5+2i

the conjugate of z2 is -5-2i

to find out the conjugate change the sign of the imaginary part

(-5,-2i)

Part B

Find out z2-z1

z1=(4,6i)

z2=(-5,2i)

so

z2-z1=(-5-4,2i-6i)

z2-z1=(-9,-4i)

to find out the coordinate of the real axis, subtract the coordinates of the real axis and to find out the coordinate of the imaginary part, subtract the coordinates of the imaginary parts