Question

if 3x+y-4i=5+(2x-3y)i, find the values of x and y.​

Answer 1

SOLUTION

GIVEN

$\sf{(3x + y) - 4i = 5 + (2x - 3y)i}$

TO DETERMINE

The values of x and y

CONCEPT TO BE IMPLEMENTED

Complex Number

A complex number z = a + ib is defined as an ordered pair of Real numbers ( a, b) that satisfies the following conditions :

(i) Condition for equality :

(a, b) = (c, d) if and only if a = c, b = d

(ii) Definition of addition :

(a, b) + (c, d) = (a+c, b+ d)

(iii) Definition of multiplication :

(a, b). (c, d) = (ac-bd , ad+bc )

Of the ordered pair (a, b) the first component a is called Real part of z and the second component b is called Imaginary part of z

EVALUATION

Here the given equality is

$\sf{(3x + y) - 4i = 5 + (2x - 3y)i}$

Comparing both sides we get

$\sf{3x + y = 5 \: \: \: \: ....(1)}$

$\sf{2x - 3y = - 4 \: \: \: ......(2)}$

Multiplying Equation (1) by 3 and Equation (2) by 1 we get

$\sf{9x +3 y = 15 \: \: \: \:}$

$\sf{2x - 3y = - 4 \: \: \:}$

On addition we get

$\sf{11x = 11}$

$\implies \sf{x = 1}$

From Equation (1) we get

$\sf{(3 \times 1) + y = 5}$

$\implies \: \sf{3 + y = 5}$

$\implies \: \sf{y = 5 - 3}$

$\implies \: \sf{y = 2}$

FINAL ANSWER

Hence the required values are

$\sf{x = 1 \: \: \: \: \: and \: \: \: y = 2}$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. If 4x + (3x – y)i = 3 – 6i , then values of x and y.

(a)x=3/4, y=33/4, (b) x=33/4, y=3/4 (c) x=-33/4, y=3 (d) x=-2, y=

https://brainly.in/question/29610963

2. Prove

z1/z2 whole bar is equal to z1 bar/z2 bar.

Bar here means conjugate

https://brainly.in/question/16314493