Question

If x+yi+1=4-3i then x= __________ and y = _______________?​

Answer 1

SOLUTION

TO FILL IN THE BLANK

If x + yi + 1 = 4 - 3i then 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 it is given that

x + yi + 1 = 4 - 3i

$\sf{ \implies \: (x + 1) + iy = 4 - 3i}$

Comparing real part and Imaginary part in both sides we get

x + 1 = 4 and y = - 3

Which gives

x = 3 and y = - 3

FINAL ANSWER

If x + yi + 1 = 4 - 3i then x = 3 and y = - 3

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