Find the complex number u , given that u ( 3 - 5 i ) = 13 + i

Given: u ( 3 - 5 i ) = 13 + i ⇒ u = 13 + i 3 - 5 i ⇒ u = ( 13 + i ) ( 3 + 5 i ) ( 3 − 5 i ) ( 3 + 5 i ) ⇒ u = 39 + 65 i + 3 i + 5 i 2 9 − 25 i 2 ⇒ u = 39 − 5 + 68 i 9 + 25 ∵ i 2 = - 1 ⇒ u = 34 + 68 i 34 ⇒ u = 1 + 2 i Hence, the complex number u = 1 + 2 i

In an electrical circuit, the voltage (volts), current (amperes) and impedance (ohms) are related by the equation voltage = current × impedance The voltage in a particular circuit is 240 V and the impedance is 48 + 36 i ohms. Find the current.

The given equation is Voltage = current × impedance ∴ Current = voltage impedance It is given that voltage = 240 V and impedance = 48 + 36 i So, current = 240 48 + 36 i = 240 ( 48 − 36 i ) ( 48 + 36 i ) ( 48 − 36 i ) = 240 ( 48 − 36 i ) 48 2 + 36 2 ∵ a 2 - b 2 = a + b a - b , i 2 = - 1 = 240 ( 48 − 36 i ) 3600 = 48 − 36 i 15 = 16 5 − 12 5 i = 3.2 − 2.4 i amperes. Hence, the current is 3.2 − 2.4 i amperes.

E M B I B E

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 11 - Complex Numbers>EXERCISE 11B>Q 7

MEDIUM

AS and A Level

IMPORTANT

Earn 100

Find the complex number $z$ satisfying the equation $z + 4 = 3 i z *$ . Give your answer in the form $x + i y,$ where $x$ and $y$ are real.

Important Questions on Complex Numbers

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 11 - Complex Numbers>EXERCISE 11B>Q 8

Find the complex number

u

, given that

(1)

MEDIUM

AS and A Level

IMPORTANT

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

z = 5 + i \sqrt{3}

is a root of a quadratic equation. Find this quadratic equation.

EASY

AS and A Level

IMPORTANT

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

In an electrical circuit, the voltage (volts), current (amperes) and impedance (ohms) are related by the equation
voltage = current

\times

impedance
The voltage in a particular circuit is

240 V

and the impedance is

48 + 36 i

ohms.
Find the current.

EASY

AS and A Level

IMPORTANT

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

Given,

u = 5 - 2 i

. On an Argand diagram, show the points

A, B, C

representing the complex numbers

u, u *

and

- u,

respectively.

EASY

AS and A Level

IMPORTANT

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

Given, $u = 5 - 2 i$ . On an Argand diagram, show the points $A, B, C$ representing the complex numbers $u, u *$ and $- u,$ respectively. The points $A B C D$ form a rectangle. Write down the complex number represented by the point $D$ .