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

AS
Answered by Adam S. Further Mathematics tutor

3841 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Find the complementary function to the second order differential equation d^2y/dx^2 - 5dy/dx + 6x = x^2


How do I differentiate tan(x) ?


How do I draw any graph my looking at its equation?


Given that α= 1+3i is a root of the equation z^3 - pz^2 + 18z - q = 0 where p and q are real, find the other roots, then p and q.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences