1. If z = x + iy is a complex number with x, y E R, we define |2| = (2² + y²)!/2 and call this quantity the modulus or absolute value of z. What is the geometric interpretation of |z|? Show that if |z| = 0, then z = : 0. Show that ifd ER, then |dz| = |A||2|, where |A| denotes the standard absolute value of a real number. (d) If z1 and z2 are two complex numbers, prove that |212| = |21||2| and |21 + z2| < |21| + |2|. (e) Show that if z + 0, then |1/2| = 1/|2|.

1. If z = x + iy is a complex number with x, y E R, we define |2| = (2² + y²)!/2 and call this quantity the modulus or absolute value of z. What is the geometric interpretation of |z|? Show that if |z| = 0, then z = : 0. Show that ifd ER, then |dz| = |A||2|, where |A| denotes the standard absolute value of a real number. (d) If z1 and z2 are two complex numbers, prove that |212| = |21||2| and |21 + z2| < |21| + |2|. (e) Show that if z + 0, then |1/2| = 1/|2|.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter7: Real And Complex Numbers

Section7.3: De Moivre’s Theorem And Roots Of Complex Numbers

Problem 9E

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