Operations with Complex Numbers (Edexcel International A Level (IAL) Further Maths: Further Pure 1): Exam Questions

In this question you must show all stages of your working.

Solutions relying entirely on calculator technology are not acceptable.

The complex number is defined by

Determine

Express in the form , where is a positive integer.

Hence find the value of

Give your answer in radians to 3 significant figures.

Given that

where is a real constant,

determine , giving your answer in the form , where and are real and in terms of .

Given also that

find the possible values of .

In this question you must show all stages of your working.

Solutions relying entirely on calculator technology are not acceptable.

Determine the exact value of

Given that

Determine in terms of and , giving your answer in the form , where

Given also that

Determine the value of and the value of

Determine , giving your answer in radians to 4 significant figures.

Given that

determine

Given also that

determine the possible values of

Show and the possible positions for on the same Argand diagram.

The complex numbers and are given by

Show and on a single Argand diagram.

Without using your calculator and showing all stages of your working,

(i) determine the value of

[1]

(ii) Express in the form

[3]

Hence determine the value of

Give your answer in radians to 2 decimal places.

The complex numbers , and are given by

where is a real number.

Find in the form where and are real. Give your answer in its simplest form in terms of .

Given that

find the possible values of p.

The complex number is defined by

where is a positive real constant.

Given that the modulus of is 5,

write down the value of

determine the argument of , giving your answer in radians to one decimal place.

In part (c) you must show detailed reasoning. Solutions relying on calculator technology are not acceptable.

Express in the form where and are real,

(i)

(ii)

Show on a single Argand diagram the points , , and that represent the complex numbers