MYTUTOR SUBJECT ANSWERS

332 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...

1 year ago

Answered by Harry, an A Level Maths tutor with MyTutor


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

334 SUBJECT SPECIALISTS

£30 /hr

Alex S.

Degree: Physics (Bachelors) - Oxford, St Peter's College University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Further Mathematics
.PAT.

“Studying Physics at the University of Oxford. Looking to tutor maths and physics at all levels, be sure to send me a message if you have any questions!”

£20 /hr

John W.

Degree: Mathematics (Masters) - St. Andrews University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“I've done a broad range of maths learning and tutoring over the years, now continuing this on to university I'm sure I'll be able to help you out!”

Maya B. GCSE Maths tutor, A Level Maths tutor, 13 Plus  Maths tutor, ...
£20 /hr

Maya B.

Degree: Mathematics with Physics (Bachelors) - Cambridge University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
.STEP.

“My approach is centred on deep understanding, and I constantly engage and encourage students to build both confidence and enthusiasm!”

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

What is an integral?

A cup of coffee is cooling down in a room following the equation x = 15 + 70e^(-t/40). Find the rate at which the temperature is decreasing when the coffee cools to 60°C.

Line AB has the equation 3x + 5y = 7. Find the gradient of Line AB.

Differentiate y = √(1 + 3x²) with respect to x

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