Given: 5.1-4.5yi=x-9i Both sides are complex numbers, and y and x are real numbers.
A complex number consists of sum of real numbers and imaginary numbers, and takes a form such as Z=a+bi. To solve this problem, change the given expression into another form of complex numbers removing the right side to left. We have:
(5.1-4.5yi)-(x-9i)=0 Combine like terms to make the expression into another form of complex numbers:
(5.1-x)+(9-4.5y)=0 ··· Eq.1 Here, let Z=0, a=5.1-x, and 9-4.5=bi.
In an expression, Z=a+bi, each term, Z, a, and bi is assumed a vector, and each vector has its own quantity and direction. Imagine a rectangle ABCD where AB represents vector a(real number), AD does vector bi(imaginary number), and the diagonal AC does vector Z(complex number).
Therefore, if Z=0, then a=0 and bi=0, so b=0 as well.
From Eq.1 we have: 5.1-x=0, and 9-4.5y=0 That is: x=5.1, and y=2
The answers are: x=5.1, and y=2