Edexcel CP2 2022 June — Question 4

Exam BoardEdexcel
ModuleCP2 (Core Pure 2)
Year2022
SessionJune
TopicComplex Numbers Argand & Loci

  1. (i) Given that
$$z _ { 1 } = 6 \mathrm { e } ^ { \frac { \pi } { 3 } \mathrm { i } } \text { and } z _ { 2 } = 6 \sqrt { 3 } \mathrm { e } ^ { \frac { 5 \pi } { 6 } \mathrm { i } }$$ show that $$z _ { 1 } + z _ { 2 } = 12 \mathrm { e } ^ { \frac { 2 \pi } { 3 } \mathrm { i } }$$ (ii) Given that $$\arg ( z - 5 ) = \frac { 2 \pi } { 3 }$$ determine the least value of \(| z |\) as \(z\) varies.