Скачать или смотреть Complex Numbers Loci Exam Question | EDEXCEL A-level Further Maths

In this detailed walkthrough, I solve a challenging complex numbers loci exam question, showing how to sketch loci on an Argand diagram and calculate the area of a complex region. This systematic approach helps students tackle one of the trickiest topics in A-level Further Mathematics.

⏱️ TIMESTAMPS:
00:00 - Introduction to complex number loci
00:25 - Identifying the equation of a circle (Part A)
01:17 - Sketching the circle on an Argand diagram
01:24 - Understanding the half-line argument condition (Part B)
02:36 - Shading the region defined by the intersection
03:14 - Approach to finding the area of the region (Part C)
04:02 - Breaking down the region into simpler parts
04:54 - Finding dimensions using coordinate geometry
05:54 - Calculating the angle using trigonometry
06:38 - Finding the area of the sector
07:23 - Calculating the area of the triangle
07:52 - Adding the quarter circle area
08:24 - Determining the total area of region A

📝 TOPICS COVERED:
Interpreting complex number equations as loci on the Argand diagram
Recognising |z-z₀| = r as the equation of a circle
Understanding arg(z-z₀) conditions as rays from a point
Finding the intersection of circular and argument loci
Breaking down complex regions into manageable parts
Using right-angled triangle properties in the complex plane
Calculating sector areas using the formula ½r²θ
Combining different area calculations for a complete solution

💯 EXAM TIPS:
Always start by identifying the standard forms of loci equations
Draw clear, labelled diagrams showing all key points and values
Break complex regions into simpler geometric shapes when calculating areas
Remember to work in radians when dealing with sector areas
Use the Pythagorean theorem to find missing dimensions
Check that your final answer has appropriate units (square units for area)
Ensure your final answer is expressed to the required degree of accuracy

As a former Head of Mathematics and A-Level Examiner, I've designed this explanation to help you tackle one of the most challenging topics in Further Mathematics with confidence.

Questions about this topic? Leave a comment below, and I'll respond personally.

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