Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
127.[HSC] (i) (ii) The complex numbers z = cos 0 + i sin 0 and w = cos α + isinα, -π<0≤π and -π<α ≤π, satisfy 1+z+w = 0. By considering the real and imaginary parts of 1+z+w, or otherwise, show that 1,z and w from the vertices of an equilateral triangle in the Argand diagram. Hence, or otherwise, show that if the three non-zero complex numbers 2i, Z₁ and Z₂ satisfy |2i| = |Z₁| = |Z₂ AND 2i+Z₁ + Z2₂ = 0 then they form the vertices of an equilateral triangle in the Argand diagram

127.[HSC] (i) (ii) The complex numbers z = cos 0 + i sin 0 and w = cos α + isinα, -π<0≤π and -π<α ≤π, satisfy 1+z+w = 0. By considering the real and imaginary parts of 1+z+w, or otherwise, show that 1,z and w from the vertices of an equilateral triangle in the Argand diagram. Hence, or otherwise, show that if the three non-zero complex numbers 2i, Z₁ and Z₂ satisfy |2i| = |Z₁| = |Z₂ AND 2i+Z₁ + Z2₂ = 0 then they form the vertices of an equilateral triangle in the Argand diagram

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.3: The Addition And Subtraction Formulas
Problem 71E
See similar textbooks
icon
Related questions
Question
127.[HSC] (i) (ii) The complex numbers z = cos 0 + i sin 0 and w = cos α + isinα, -π<0≤π and -π<α ≤π, satisfy 1+z+w = 0. By considering the real and imaginary parts of 1+z+w, or otherwise, show that 1,z and w from the vertices of an equilateral triangle in the Argand diagram. Hence, or otherwise, show that if the three non-zero complex numbers 2i, Z₁ and Z₂ satisfy |2i| = |Z₁| = |Z₂ AND 2i+Z₁ + Z2₂ = 0 then they form the vertices of an equilateral triangle in the Argand diagram
Transcribed Image Text:127.[HSC] (i) (ii) The complex numbers z = cos 0 + i sin 0 and w = cos α + isinα, -π<0≤π and -π<α ≤π, satisfy 1+z+w = 0. By considering the real and imaginary parts of 1+z+w, or otherwise, show that 1,z and w from the vertices of an equilateral triangle in the Argand diagram. Hence, or otherwise, show that if the three non-zero complex numbers 2i, Z₁ and Z₂ satisfy |2i| = |Z₁| = |Z₂ AND 2i+Z₁ + Z2₂ = 0 then they form the vertices of an equilateral triangle in the Argand diagram
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS