math problem What is the complex number a-bi if (2-i)(a-bi) = 2+9i

Expert Answers

An illustration of the letter 'A' in a speech bubbles

We have to determine a-bi if (2-i)(a-bi) = 2+9i

(2-i)(a-bi) = 2+9i

=> 2a - 2bi - ai + bi^2 = 2 + 9i

=> 2a - b - 2bi - ai = 2 + 9i

Equating the real and imaginary coefficients we get

2a - b = 2 and...

Unlock
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your 48-Hour Free Trial

We have to determine a-bi if (2-i)(a-bi) = 2+9i

(2-i)(a-bi) = 2+9i

=> 2a - 2bi - ai + bi^2 = 2 + 9i

=> 2a - b - 2bi - ai = 2 + 9i

Equating the real and imaginary coefficients we get

2a - b = 2 and 2b + a = -9

=> 2(-2b - 9) - b = 2

=> -4b - 18 - b = 2

=> -5b = 20

=> b = -4

a = 8 - 9 = -1

The required number a + bi = -1 - 4i

Approved by eNotes Editorial Team