What is the answer to (x+y)-(3x+2y)i=5+2i ?

The answer to (x+y)-(3x+2y)i=5+2i is x=-12,y=17

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(x+y)-(3x+2y)i=5+2i

(x + y) - (3 x + 2 y) i = 5 + 2 i

x = - 12, y = 17

Solution steps

(x + y) - (3 x + 2 y) i = 5 + 2 i

Rewrite

(x + y) - (3 x + 2 y) i

in standard complex form:

(x + y) + (- 3 x - 2 y) i

(x + y) + (- 3 x - 2 y) i = 5 + 2 i

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

[x + y = 5 - 3 x - 2 y = 2]

[x + y = 5 - 3 x - 2 y = 2] : x = - 12, y = 17

x = - 12, y = 17

z^{2} - (2 - i) z + (3 - i) = 0

(2 x - 5 i y) (1 + i)^{2} = 10 (2 + i)

z^{2} = 3 + i

z^{2} + (2 i - 3) + 5 - i = 0

7 + i^{3} - x i = 9 - i^{3} - x i

What is the answer to (x+y)-(3x+2y)i=5+2i ?
The answer to (x+y)-(3x+2y)i=5+2i is x=-12,y=17