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Find the values of x and y which satisfy the following equations (x, y ∈ R): (x + 2y) + (2x – 3y i + 4i = 5 - Mathematics and Statistics

Sum

Find the values of x and y which satisfy the following equations (x, y ∈ R): (x + 2y) + (2x – 3y i + 4i = 5

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Solution

(x + 2y) + (2x – 3y i + 4i = 5
∴ (x + 2y) + (2x – 3y)i = 5 – 4i
Equating real and imaginary parts, we get
x + 2y = 5               ...(i)
and 2x - 3y = – 4   ...(ii)
Equation (i) x 2 – equation (ii) gives
7y = 14
∴ y = 2
Putting y = 2 in (i), we get
x + 2(2) = 5
∴ x + 4 = 5
∴ x = 1
∴ x = 1 and y = 2.

Concept: Solution of a Quadratic Equation in Complex Number System
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board
Chapter 3 Complex Numbers
Exercise 3.1 | Q 8. (i) | Page 38
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