What is the answer to (x+6i)=(3-i)+(4-2yi) ?

The answer to (x+6i)=(3-i)+(4-2yi) is x=7,y=-7/2

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(x+6i)=(3-i)+(4-2yi)

(x + 6 i) = (3 - i) + (4 - 2 y i)

x = 7, y = - \frac{7}{2}

Solution steps

(x + 6 i) = (3 - i) + (4 - 2 y i)

Rewrite

(x + 6 i)

in standard complex form:

x + 6 i

x + 6 i = (3 - i) + (4 - 2 y i)

Rewrite

(3 - i) + (4 - 2 y i)

in standard complex form:

7 + (- 1 - 2 y) i

x + 6 i = 7 + (- 1 - 2 y) i

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

[x = 7 6 = - 1 - 2 y]

[x = 7 6 = - 1 - 2 y] : x = 7, y = - \frac{7}{2}

x = 7, y = - \frac{7}{2}

(3 + 4 i)^{2} - 2 (x - i y) = x + i y

3 x - y - i = 2 i x - i y

x^{2} - 8 i x - 25 = 0

- 4 + (y) i = - 12 x - i + 8

z^{2} - (3 + 5 i) z + 8 i - 5 = 0

What is the answer to (x+6i)=(3-i)+(4-2yi) ?
The answer to (x+6i)=(3-i)+(4-2yi) is x=7,y=-7/2