Solve the following equation for x, y ∈ R: x+iy2+3i = 7 – i - Mathematics and Statistics

Question

Solve the following equation for x, y ∈ R:

`(x + "i"y)/(2 + 3"i")` = 7 – i

Sum

Solution

`(x + "i"y)/(2 + 3"i")` = 7 – i

∴ x + iy = (7 – i)(2 + 3i)
∴ x + iy = 14 + 21i – 2i – 3i²
∴ x + iy = 14 + 19i – 3(– 1) ...[∵ i² = – 1]
∴ x + iy = 17 + 19i
Equating real and imaginary parts, we get
x = 17 and y = 19

shaalaa.com

Solution of a Quadratic Equation in Complex Number System

Is there an error in this question or solution?

Q 4) iii)Q 4) ii)Q 4) iv)

Chapter 3: Complex Numbers - MISCELLANEOUS EXERCISE - 3 [Page 43]

APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) [English] 11 Standard Maharashtra State Board

Chapter 3 Complex Numbers
MISCELLANEOUS EXERCISE - 3 | Q 4) iii) | Page 43

RELATED QUESTIONS

Find the values of x and y which satisfy the following equations (x, y ∈ R):

`(x + 1)/(1 + "i") + (y - 1)/(1 - "i")` = i

Solve the following quadratic equation:

`2x^2 - sqrt(3) x + 1` = 0

Solve the following quadratic equation:

x² – 4x + 13 = 0

Solve the following quadratic equation:

x² + 3ix + 10 = 0

Solve the following quadratic equation:

x² – (2 + i) x – (1 – 7i) = 0

Solve the following quadratic equation:

`x^2 - (3 sqrt(2) + 2"i") x + 6 sqrt(2)"i"` = 0

Solve the following quadratic equation:

(2 + i) x² – (5 – i) x + 2(1 – i) = 0

Solve the following equation for x, y ∈ R:

(1 – 3i) x + (2 + 5i) y = 7 + i

Solve the following equation for x, y ∈ R:

(x + iy)(5 + 6i) = 2 + 3i

Solve the following equation for x, y ∈ R:

2x + i⁹ y (2 + i) = x i⁷ + 10 i¹⁶

Solve the following quadratic equations.

8x² + 2x + 1 = 0