Let z and zo be two complex numbers. It is given that |z| = 1 and the numbers z, zo, zzo, 1, and 0 are represented in an Argano diagram by the points P, Po, Q, A, and the origin, respectively Show that the triangles POP, and AOQ are congruent. Hence or otherwise, prove that |z-zol = |zzo - 11. 0

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.3: Trigonometric Functions Of Real Numbers
Problem 38E
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Let z and zo be two complex numbers. It is given that |z| = 1 and
the numbers z, zo, zzo, 1, and 0 are represented in an Argand
diagram by the points P, Po, Q, A, and the origin, respectively.
Show that the triangles POP, and AOQ are congruent. Hence,
or otherwise, prove that |z-zol = |zzo - 11.
Transcribed Image Text:Let z and zo be two complex numbers. It is given that |z| = 1 and the numbers z, zo, zzo, 1, and 0 are represented in an Argand diagram by the points P, Po, Q, A, and the origin, respectively. Show that the triangles POP, and AOQ are congruent. Hence, or otherwise, prove that |z-zol = |zzo - 11.
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