How do I solve 5.1-4.5yi=x-9i?

Question

I don't know the first step to take in this equation. Someone please help.

Answer 1

5.1 -4.5iy =(x-9i)

-4.5iy=x-5.1 -9i

(-4.5)(-1)y=i*(x-5.1 -9i)

4.5y=ix -5.1i+9

y=(ix/4.5) -(5.1/4.5)i +(9/4.5)

=2 +(ix/4.5) -1.13333333333i

=2+(0.22222222222x -1.133333333)i

Answer 2

Given: 5.1-4.5yi=x-9i   Both sides are complex numbers, and yand x are real numbers.

Acomplex nomber 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   Cobine like terms to make this into another form of complex numbers:

(5.1-x) +(9-4.5y)i=0 ··· Eq.1   Here, let Z=0, a=5.1-x, and b=9-4.5y.

In an explession, 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 side AB represents vector a(real number), side AD does a vector bi(imaginary number), and diagonal AC does 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

Answer 3

Given: 5.1-4.5yi=x-9i

Both sides are complex numbers, consist of real numbers and imaginary numbers.   5.1 and x represent real numbers, and -4.5yi and -9i represent imaginary numbers.

If 2 complex numbers are equal, the real parts and imaginary parts are equal separately.

Thus, 5.1=x and -4.5yi=-9i.   That is: x=5.1 and 4.5y=9, so y=9/4.5=2

The answers are: x=5.1 and y=2　　

Answer 4

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