Question

Find x and y such that 2x + 3iy nad 2+9i represents the same complex number

Answer 1

Answer:

2x=2 --> x = 1

3y = 9  y = 3

Answer 2

The value of x = 1 & y = 3

Given :

2x + 3iy and 2 + 9i represents the same complex number

To find :

The value of x and y

Concept :

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 )

Solution :

Step 1 of 2 :

Write down the given data

Here it is given that 2x + 3iy and 2 + 9i represents the same complex number

Step 2 of 2 :

Find the value of x and y

From property of complex number

2x + 3iy = 2 + 9i gives

2x = 2 & 3y = 9

Which gives x = 1 & y = 3

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