OCR
Further Pure Core AS
2021
November
— Question 4
Exam Board
OCR
Module
Further Pure Core AS (Further Pure Core AS)
Year
2021
Session
November
Topic
Complex Numbers Argand & Loci
4
A locus \(C _ { 1 }\) is defined by \(C _ { 1 } = \{ \mathrm { z } : | \mathrm { z } + \mathrm { i } | \leqslant \mid \mathrm { z } - 2 \}\).
Indicate by shading on the Argand diagram in the Printed Answer Booklet the region representing \(C _ { 1 }\).
Find the cartesian equation of the boundary line of the region representing \(C _ { 1 }\), giving your answer in the form \(a x + b y + c = 0\).
A locus \(C _ { 2 }\) is defined by \(C _ { 2 } = \{ \mathrm { z } : | \mathrm { z } + 1 | \leqslant 3 \} \cap \{ \mathrm { z } : | \mathrm { z } - 2 \mathrm { i } | \geqslant 2 \}\).
Indicate by shading on the Argand diagram in the Printed Answer Booklet the region representing \(C _ { 2 }\).