Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 11 - Complex Numbers>EXERCISE 11D>Q 9

MEDIUM

AS and A Level

IMPORTANT

Earn 100

Given that $z^{3} - 12 z^{2} + p z + q = 0$ where $p$ and $q$ are real constants. It is given that $z = 2 + i$ is a root of the equation. Find the value of $p$ and the value of $q$ .

Important Questions on Complex Numbers

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 11 - Complex Numbers>EXERCISE 11D>Q 9

Given that

z^{3} - 12 z^{2} + p z + q = 0

where

p

and

q

are real constants. It is given that

z = 2 + i

is a root of the equation. Find the value of

p

and the value of

q

.

Represent the roots of this equation on an Argand diagram.

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 11 - Complex Numbers>EXERCISE 11D>Q 10

f (z) = z^{4} - z^{3} + 20 z^{2} - 16 z + 64 = (z^{2} + a) (z^{2} + b z + 4)

Solve the equation

f (z) = 0 .

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 11 - Complex Numbers>EXERCISE 11E>Q 1

Describe, in words, the locus represented by

\arg (z - 2 + 3 i) = \frac{π}{12}

.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 11 - Complex Numbers>EXERCISE 11E>Q 1

Describe, in words, the locus represented by

| z - 10 | < | z - 6 i |

.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 11 - Complex Numbers>EXERCISE 11E>Q 1

Describe, in words, the locus represented by

| z + 6 - i | = 7

.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 11 - Complex Numbers>EXERCISE 11E>Q 1

Describe, in words, the locus represented by the following.

\arg (z) = \frac{5 π}{12}

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 11 - Complex Numbers>EXERCISE 11E>Q 2

On an Argand diagram, sketch the following locus. Shade any region where it is needed.

| z - (2 + i) | = | z - (4 + 3 i) |

.

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 11 - Complex Numbers>EXERCISE 11E>Q 2

On an Argand diagram, sketch the following locus. Shade any region where it is needed.

\arg (z + 3 i) = - \frac{π}{3}

.