LOCUS IN THE COMPLEX PLANE The locus defines the path of a complex number Recall from the start of the chapter that the modulus and the argument defines.

Slides:



Advertisements
Similar presentations
Polarization of EM waves
Advertisements

1. 6 Circles (Part 1) 1. Circle Notes
Complex Numbers If we wish to work with , we need to extend the set of real numbers Definitions i is a number such that i2 = -1 C is the set of.
5 Locus Contents 5.1 Introduction to Locus
Problem Set 2, Problem # 2 Ellen Dickerson. Problem Set 2, Problem #2 Find the equations of the lines that pass through the point (1,3) and are tangent.
Notes Over 10.3 r is the radius radius is 4 units
The Circle (x 1, y 1 ) (x 2, y 2 ) If we rotate this line we will get a circle whose radius is the length of the line.
CIRCLES.
ENS 207 engineering graphics
Complex Loci – Modulus Question
Coordinate Geometry – The Circle
Graphing Circles Viviana C. Castellón East Los Angeles College MEnTe Mathematics Enrichment through Technology.
Definition: A circle is the set of all points on a plane that is a fixed distance from the center.
Properties of Circles Perimeter and Area A circle is defined as a plane curve formed by the set of all points which are a given fixed distance from a.
Mathematics.
3.4 Area and Circumference 1 Circle A circle is a plane figure that consists of all points that lie the same distance from a fixed point. The fixed point.
11.4: Circumference and Arc Length Objectives: Develop and apply the equation for the circumference of a circle Determine arc length of a circle Common.
10.6 Equations of a Circle Standard Equation of a Circle Definition of a Circle.
Equations of Circles 10.6 California State Standards 17: Prove theorems using coordinate geometry.
EXAMPLE 1 Write an equation of a circle Write the equation of the circle shown. The radius is 3 and the center is at the origin. x 2 + y 2 = r 2 x 2 +
Pupils notes for Circle Lessons.  The equation of a circle with centre ( a, b ) and radius r is We usually leave the equation in this form without multiplying.
C2: Coordinate Geometry of the Circle Learning Objective: To be able to find and use the equation of a circle.
9-8 Equations of Circles Objectives: To write and use the equation of a circle in the coordinate plane.
Chapter 10 Lesson 1: Circles and Circumference Objective: Learn to find the circumference of circles.
Copyright © 2011 Pearson, Inc. 6.6 De Moivre’s Theorem and nth Roots.
Chapter Surface Area and Volume of Spheres.
1 (1) Indefinite Integration (2) Cauchy’s Integral Formula (3) Formulas for the derivatives of an analytic function Section 5 SECTION 5 Complex Integration.
The circumference of the circle is 50  feet. The area of the shaded region = ________ example 1 :
1.4 – Rewrite Formulas and Equations. Example 1: Solve the formula C = 2pir for r. Then find the radius of a circle with a circumference of 44 inches.
How is a circle different from a line? Equation of a circle is more involved, and more complex than a straight line.
RADIANS Radians, like degrees, are a way of measuring angles.
Circumferences & Areas of Circles. Circle information Defn: Points on a plane that are equidistant from a given point (CENTER). Radius: From center to.
CIRCLE Circle is the locus Of all poins equidistant From a central poins.
Circles in the Coordinate Plane I can identify and understand equations for circles.
Question 1 Write the equation of the circle: Center: (-7, 14) Area: 81π.
SUBMITTED BY ROSHNI B S. Circle is a closed curve in a plane A circle can be drawn with the help of a circular object.
Write and Graph Equations of Circles Chapter 10: Circles.
Algebra II Honors Problem of the Day Homework: p odds Without graphing find all symmetries for each equation.
Warm-Up Find the distance and the midpoint. 1. (0, 3) and (3, 4)
Equations of Circles. Vocab Review: Circle The set of all points a fixed distance r from a point (h, k), where r is the radius of the circle and the point.
GeometryGeometry 10.7 Locus. GeometryGeometry Drawing a Locus that Satisfies One Condition A locus in a plane is a set of all points in a plane that satisfy.
The Equation of a Circle. Aims To recognise the equation of a circle To find the centre and radius of a circle given its equation To use the properties.
The Circle. Examples (1) – (5) Determine the center and radius of the circle having the given equation. Identify four points of the circle.
9.6 Circles in the Coordinate Plane Date: ____________.
8.1 The Rectangular Coordinate System and Circles Part 2: Circles.
Chapter 10.7 Notes: Write and Graph Equations of Circles
Equations of Circles. You can write an equation of a circle in a coordinate plane, if you know: Its radius The coordinates of its center.
CHAPTER 1 COMPLEX NUMBER. CHAPTER OUTLINE 1.1 INTRODUCTION AND DEFINITIONS 1.2 OPERATIONS OF COMPLEX NUMBERS 1.3 THE COMPLEX PLANE 1.4 THE MODULUS AND.
Circle Radius Diameter Tangent Circumference. Angles subtended by the same chord are equal Chord.
Higher Maths 2 4 Circles1. Distance Between Two Points 2Higher Maths 2 4 Circles The Distance Formula d =d = ( y2 – y1)²( y2 – y1)² + ( x2 – x1)²( x2.
Geometric Probability Probability Recall that the probability of an event is the likelihood that the event will occur.
Equation of a Circle. Equation Where the center of the circle is (h, k) and r is the radius.
EXAMPLE 1 Write an equation of a circle Write the equation of the circle shown. SOLUTION The radius is 3 and the center is at the origin. x 2 + y 2 = r.
Objective: Solve equations using area circumference, diameter, and radius.
MATHPOWER TM 12, WESTERN EDITION Chapter 3 Conics.
Circles A review?. Let's review what we already know about circles. Definition: A circle is a locus (set) of points in a plane equidistant from a fixed.
  Where the center of the circle is (h, k) and r is the radius. Equation.
Advanced Algebra H Notes Section 9.3 – Graph and Write Equations of Circles Objective: Be able to graph and write equations of circles. A _________ is.
Welcome. Teacher’s Introduction Md. Shamsuzzaman Lecturer (Mathematics) Joypurhat Girls’ Cadet College Mobile:
8.1 The Rectangular Coordinate System and Circles Part 2: Circles.
+ Equation of a Circle. + Circle A Circle is a set of all points in a plane equidistant from a given point. The Center.
CHAPTER 1 COMPLEX NUMBERS
CHAPTER 1 COMPLEX NUMBERS
CHAPTER 1 COMPLEX NUMBERS
Warm Up May 14th Find the area and circumference of a circle with a diameter of 9 in. Find the area of a circle is the circumference is 41 ft. Find.
Equation of a Circle.
10-7: Write and Graph Equations of Circles
Objective: To know the equations of simple straight lines.
Calculate the distance of this point from the origin
Objective: To know the equations of simple straight lines.
Presentation transcript:

LOCUS IN THE COMPLEX PLANE The locus defines the path of a complex number Recall from the start of the chapter that the modulus and the argument defines the position of a ‘z’ Also recall that the equation of a circle with radius ‘r’ and centre (a,b)

The complex number z moves in the complex plane subject to the condition Find the equation of the locus of z and interpret the locus geometrically. The locus of the complex number ‘z’ is therefore the points on the circle centre the origin and radius r = 9

The complex number z moves in the complex plane subject to the condition. Find the equation of the locus of z and interpret the locus geometrically. The locus of z is the set of points on the circumference of the circle with centre (1, 2) and radius 4.

The complex number z moves in the complex plane subject to the condition Find the equation of the locus of z and interpret the locus geometrically. The locus of z is the set of points which lie inside the circle with centre (0, 1) and radius 2. [Note that if the condition was the locus of z would be the set of points which lie on or inside the circle with centre O and radius 2.]

The complex number z moves in the complex plane subject to the condition. Find the equation of the locus of z and interpret the locus geometrically. The locus of z is the straight line.

The complex number z moves in the complex plane such that Show that the locus of z is a straight line and find the equation of the locus of z. The equation of the locus of z is

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2025 SlidePlayer.com. Inc. All rights reserved.