MYTUTOR SUBJECT ANSWERS

612 views

Given that abc = -37 + 36i; b = -2 + 3i; c = 1 + 2i, what is a?

Substituting the given values for b and c into the equation for abc,

a(-2 + 3i)(1 + 2i) = -37 + 36i

Multiplying out the terms in brackets,

a(-2 - 4i + 3i - 6) = -37 + 36i

Collecting like terms and multiplying through by -1,

a(8 + i) = 37 - 36i

The complex number a can be represented as m + ni, where m and n are constants we need to find.

(8 + i)(m + ni) = 37 - 36i

Multiplying out the terms in brackets,

8m + 8ni + mi - n = 37 - 36i

Collecting like terms and equating the real and imaginary parts, we end up with two simultaneous equations for m and n.

8m - n = 37 (from real part)

8n + m = -36 (from imaginary part)

Rearranging the first equation, we find that n = 8m - 37. Substituting this into the second equation,

8(8m - 37) + m = -36

64m - 296 + m = -36

65m - 296 = -36

65m = 260

m = 4

Subsituting this value for m back into the second equation,

8n + 4 = -36

8n = -40

n = -5

Putting it all together,

a = 4 - 5i

Adam S. A Level Further Mathematics  tutor, A Level Maths tutor, A Le...

2 years ago

Answered by Adam, an A Level Further Mathematics tutor with MyTutor


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

116 SUBJECT SPECIALISTS

£20 /hr

Praveenaa K.

Degree: Mathematics (Masters) - Bristol University

Subjects offered:Further Mathematics , Science+ 4 more

Further Mathematics
Science
Maths
English
Chemistry
-Personal Statements-

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

£24 /hr

Ayusha A.

Degree: BEng electrical and electronics engineering (Bachelors) - Newcastle University

Subjects offered:Further Mathematics , Physics+ 1 more

Further Mathematics
Physics
Maths

“About me: I am a final year Electrical and Electronic Engineering student at Newcastle University. I took Mathematics, Further Mathematics, Chemistry and Physics as my A-level subjects. I did peer mentoring in university and also have...”

£26 /hr

Hannah B.

Degree: MMath(Hons) in Mathematics (Other) - Manchester University

Subjects offered:Further Mathematics , Maths+ 1 more

Further Mathematics
Maths
-Personal Statements-

“Top tutor from the renowned Russell Group university, ready to help you improve your grades.”

About the author

Adam S.

Currently unavailable: for regular students

Degree: Artificial Intelligence (Masters) - York University

Subjects offered:Further Mathematics , Physics+ 1 more

Further Mathematics
Physics
Maths

“I love maths and physics. I loved them as a child, I loved them at university and I even loved them at school. I hope that during my tutorials you will grow to love these subjects too. About me I graduated from the University of York...”

You may also like...

Posts by Adam

Given that abc = -37 + 36i; b = -2 + 3i; c = 1 + 2i, what is a?

Given that y = exp(2x) * (x^2 +1)^(5/2), what is dy/dx when x is 0?

Other A Level Further Mathematics questions

What is De Moivre's theorem?

Prove by mathematical induction that, for all non-negative integers n, 11^(2n) + 25^n + 22 is divisible by 24

How do I do a proof by induction?

Prove e^(ix) = cos (x) + isin(x)

View A Level Further Mathematics 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