What is the answer to 3x+y+(2x+2y)i=13 ?

The answer to 3x+y+(2x+2y)i=13 is x= 13/2 ,y=-13/2

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3x+y+(2x+2y)i=13

3 x + y + (2 x + 2 y) i = 13

x = \frac{13}{2}, y = - \frac{13}{2}

Solution steps

3 x + y + (2 x + 2 y) i = 13

Rewrite

13

in standard complex form:

13 + 0 i

3 x + y + (2 x + 2 y) i = 13 + 0 i

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

[3 x + y = 13 2 x + 2 y = 0]

[3 x + y = 13 2 x + 2 y = 0] : x = \frac{13}{2}, y = - \frac{13}{2}

x = \frac{13}{2}, y = - \frac{13}{2}

\frac{x ^{2} - 5}{2 x + i} = 0

2 x + 2 y = 2 x + 2 y i + 10

2 (a + ib)^{2} + 2 (a + ib) + 13 = 0

R, ii R + i q = e

∣ z - (3 + 2 i) ∣ = 2

What is the answer to 3x+y+(2x+2y)i=13 ?
The answer to 3x+y+(2x+2y)i=13 is x= 13/2 ,y=-13/2