The remainder of this question concerns the complex numbers z₁ = 3+j3 and Z₂ = -1-j -j2. (b) Calculate (i) Z₁ + Z₂, (ii) Z₁ Z2, (iii) Z₁/Z2, giving your answers in the form a + jb where a and b are real numbers. (c) (i) Express z₁ in exponential form. (Keep the modulus and argument in exact form.) (ii) Express z₂ in polar form. (Evaluate the modulus to two decimal places. Evaluate the argument in degrees to two decimal places in the range 0 ≤ arg (Z₂) < 360°.) (d) Find the five distinct fifth roots of z₁, expressing your answers in exact exponential form with arguments in the range 0 ≤ arg (z) < 2. (e) Sketch the locus of the points z in the complex plane that satisfy the equation Z + Z₁ Z + Z₂ = 3.
The remainder of this question concerns the complex numbers z₁ = 3+j3 and Z₂ = -1-j -j2. (b) Calculate (i) Z₁ + Z₂, (ii) Z₁ Z2, (iii) Z₁/Z2, giving your answers in the form a + jb where a and b are real numbers. (c) (i) Express z₁ in exponential form. (Keep the modulus and argument in exact form.) (ii) Express z₂ in polar form. (Evaluate the modulus to two decimal places. Evaluate the argument in degrees to two decimal places in the range 0 ≤ arg (Z₂) < 360°.) (d) Find the five distinct fifth roots of z₁, expressing your answers in exact exponential form with arguments in the range 0 ≤ arg (z) < 2. (e) Sketch the locus of the points z in the complex plane that satisfy the equation Z + Z₁ Z + Z₂ = 3.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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maths help can you do d)and e) please
Transcribed Image Text:The remainder of this question concerns the complex numbers z₁ = 3+j3 and Z₂ = − 1 − j2.
(b) Calculate
(i) Z₁ + Z₂,
(ii) Z₁ Z2,
(iii) Z₁/Z2,
giving your answers in the form a + jb where a and b are real numbers.
(c) (i) Express z₁ in exponential form. (Keep the modulus and argument in exact form.)
(ii) Express z₂ in polar form. (Evaluate the modulus to two decimal places. Evaluate
the argument in degrees to two decimal places in the range 0 ≤ arg(z₂) < 360°.)
(d) Find the five distinct fifth roots of z₁, expressing your answers in exact exponential
form with arguments in the range 0 ≤ arg (z) < 2π.
(e) Sketch the locus of the points z in the complex plane that satisfy the equation
Z + Z₁
Z + Z₂
= 3.
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