MYTUTOR SUBJECT ANSWERS

214 views

Rationalise the complex fraction: (8 + 6i)/(6 - 2i)

The problem with this fraction is the "i" on the denominator, it is not rational. To rationalise this fraction we use the complex conjugate.

This sounds more complicated than it is. If a + ib is a complex number, then a - ib is its conjugate. The only thing that changes is that the imaginary part of the number changes its sign.

To rationalise the fraction you multiply both top and bottom of the fraction by the the complex conjugate of the denominator.

(8 + 6i)/(6 - 2i) * (6 + 2i)/(6 + 2i)

To make this less messy in text I will solve the top and bottom separately. First the top:

(8 + 6i)*(6 + 2i) = 48 + 16i + 36i + 12i^2 = 48 + 52i - 12 = 36 + 52i

Then the bottom:

(6 - 2i)*(6 + 2i) = 36 - 12i + 12i - 4i^2 = 36 + 4 = 40

Putting these together gives:

(36 + 52i)/40 

Simplified this is:

9/10 + (13/10)i

Harry C. GCSE Further Mathematics  tutor, A Level Further Mathematics...

10 months ago

Answered by Harry, an A Level Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

270 SUBJECT SPECIALISTS

£24 /hr

Tiarnan B.

Degree: MChem (Masters) - York University

Subjects offered:Maths, Geography+ 2 more

Maths
Geography
Chemistry
-Personal Statements-

“I am a fun, open and qualified tutor. I guarantee by choosing me you will reach where you want to be and beyond, all while enjoying the subject!”

£24 /hr

Eilidh F.

Degree: Natural Sciences (Bachelors) - York University

Subjects offered:Maths, Further Mathematics + 2 more

Maths
Further Mathematics
Chemistry
Biology

“About me: My name is Eilidh (pronounced Aylee) and I am a student at the University of York. I study Natural Sciences specialising in Neuroscience, and have always loved both Science and Maths. I also reallyenjoy teaching, meeting new...”

Sam C. GCSE Maths tutor, 13 Plus  Maths tutor, 11 Plus Maths tutor, A...
£20 /hr

Sam C.

Degree: Physics (Masters) - Oxford, Trinity College University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
.PAT.
-Oxbridge Preparation-

“Maths and Physics hold the tools to unravelling the mysteries of the universe! I hope you enjoy unlocking these tools as much as I do!”

About the author

Harry C.

Currently unavailable: for new students

Degree: Engineering (Masters) - Durham University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“About me: I am a student at Durham University doing a master’s degree in Aeronautical Engineering. I’m in my final year and I’ve thoroughly enjoyed my time here. I really enjoy maths and physics and I’m hopefully quite good at both by...”

You may also like...

Posts by Harry

Explain the different types of wave.

Find the maximum or minimum value of the function: y = 6x^2 + 4x + 2

Rationalise the complex fraction: (8 + 6i)/(6 - 2i)

Other A Level Maths questions

How do I use the chain rule to differentiate polynomial powers of e?

How do I do integration by parts?

What is the sum of the first 10 terms of the geometric series 32 + 16 + 8 + ... ?

Find the coordinates of the minimum point of the curve y = 3x^(2) + 9x + 10

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok