MYTUTOR SUBJECT ANSWERS

274 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...

1 year 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

66 SUBJECT SPECIALISTS

£20 /hr

Solomon L.

Degree: Mathematics (Bachelors) - Leeds University

Subjects offered: Further Mathematics , Maths

Further Mathematics
Maths

“Currently studying at Leeds university, ready to help you improve your grades in Maths and Chemistry GCSE! ”

£20 /hr

Michael F.

Degree: Mathematics (Bachelors) - Oxford, Pembroke College University

Subjects offered: Further Mathematics , Maths

Further Mathematics
Maths

“Personal Description: I am about to start my first year of studying Maths at Oxford University. I enjoy teaching Maths and have been extremely passionate about it since the start of my academic career. I am here to help students of an...”

£20 /hr

Guy P.

Degree: Mathematics (Masters) - Warwick University

Subjects offered: Further Mathematics , Maths+ 2 more

Further Mathematics
Maths
.STEP.
.MAT.

“About:Hi. I am a 2nd Year Mathematics student at the University of Warwick. I achieved a comfortable First in Year 1 and have continued this trend into my second year. Even from an early age, I have had a burning passion to engage m...”

About the author

Adam S.

Currently unavailable: for regular students

Degree: Artificial Intelligence (Masters) - Edinburgh 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

Find the nth roots of unity.

The roots of the equation z^3 + 2z^2 +3z - 4 = 0, are a, b and c . Show that a^2 + b^2 +c^2 = -2

Convert the general complex number z=x+iy to modulus-argument form.

Understanding differentiation from first principle.

View A Level Further Mathematics tutors

Cookies:

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

mtw:mercury1:status:ok