What is the answer to 3(x-2)=2yi-(1-i),y+2=x-3i ?

The answer to 3(x-2)=2yi-(1-i),y+2=x-3i is x= 5/3 ,y=-1/2

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3(x-2)=2yi-(1-i),y+2=x-3i

3 (x - 2) = 2 y i - (1 - i), y + 2 = x - 3 i

x = \frac{5}{3}, y = - \frac{1}{2}

Solution steps

3 (x - 2) = 2 y i - (1 - i)

Rewrite

3 (x - 2)

in standard complex form:

3 (x - 2) + 0 i

3 (x - 2) + 0 i = 2 y i - (1 - i)

Rewrite

2 y i - (1 - i)

in standard complex form:

- 1 + (2 y + 1) i

3 (x - 2) + 0 i = - 1 + (2 y + 1) i

Complex numbers can be equal only if their real and imaginary parts are equalRewrite as system of equations:

[3 (x - 2) = - 1 0 = 2 y + 1]

[3 (x - 2) = - 1 0 = 2 y + 1] : x = \frac{5}{3}, y = - \frac{1}{2}

x = \frac{5}{3}, y = - \frac{1}{2}

a, z = (a + bi) (a - bi)

\frac{Z - i}{Z} = 2 + i

5 x + 3 i = 15 + y i

i (t) = t^{2} - 5 t + 6

x = 0 + i y - 2 x + 2 i y + 7 - 6 i

What is the answer to 3(x-2)=2yi-(1-i),y+2=x-3i ?
The answer to 3(x-2)=2yi-(1-i),y+2=x-3i is x= 5/3 ,y=-1/2