Discovery Lesson |z-z1|=n

Instructions for the graph below

1. Set n to 3. [br][br]2. Drag the point z around the screen. When it is black then [math]|z|=3[/math]. When it is red then [math]|z|\ne3[/math][br][br]3. Find all the black points that satisfy [math]|z|=3[/math][br][br]4. Repeat for [math]|z|=6[/math][br]

Describe the locus of points defined b[math]|z|=n[/math]

Explain why [math]|z|=n[/math] creates the shape you described in the previous question.

Instructions for the graph below

1. Move [math]z_{_{_1}}[/math] to the point 4+2i. [br][br]2. Set n to 3. [br][br]2. Drag the point z around the screen. When it is black then [math]|z-z_1|=3[/math]. When it is red then [math]|z-z_1|\ne3[/math][br][br]3. Find all the black points that satisfy [math]|z-z_1|=3[/math][br][br]4. Repeat for [math]|z-z_1|=6[/math][br][br]5. Repeat for [math]n=4[/math] and [math]z_1=-2-3i[/math][br]

Describe the locus of points defined by [math]|z-z_1|=n[/math]

Explain why [math]|z-z_1|=n[/math] creates the shape you described in the previous question.

Discovery Lesson |z-z1|=n

Instructions for the graph below

Instructions for the graph below

Question 1

Question 2

Question 3

Question 4

Question 5

Informação: Discovery Lesson |z-z1|=n