Multi-part questions with division as one step

Questions where division of complex numbers is one part of a larger multi-part question that also involves other operations like addition, multiplication, powers, modulus, or argument.

27 questions

OCR FP1 AS 2021 June Q2
2 In this question you must show detailed reasoning.
The complex number \(7 - 4 \mathrm { i }\) is denoted by \(z\).
  1. Giving your answers in the form \(a + b \mathrm { i }\), where \(a\) and \(b\) are rational numbers, find the following.
    1. \(3 z - 4 z ^ { * }\)
    2. \(( z + 1 - 3 \mathrm { i } ) ^ { 2 }\)
    3. \(\frac { z + 1 } { z - 1 }\)
  2. Express \(z\) in modulus-argument form giving the modulus exactly and the argument correct to 3 significant figures.
  3. The complex number \(\omega\) is such that \(z \omega = \sqrt { 585 } ( \cos ( 0.5 ) + \mathrm { i } \sin ( 0.5 ) )\). Find the following.
    • \(| \omega |\)
    • \(\arg ( \omega )\), giving your answer correct to 3 significant figures
OCR FP1 AS 2017 Specimen Q2
2 In this question you must show detailed reasoning.
Given that \(z _ { 1 } = 3 + 2 \mathrm { i }\) and \(z _ { 2 } = - 1 - \mathrm { i }\), find the following, giving each in the form \(a + b \mathrm { i }\).
  1. \(\mathrm { z } _ { 1 } { } ^ { * } \mathrm { z } _ { 2 }\)
  2. \(\frac { z _ { 1 } + 2 z _ { 2 } } { z _ { 2 } }\)