What is the answer to 3(x+5i)=7yi-6+8 ?

The answer to 3(x+5i)=7yi-6+8 is x= 2/3 ,y= 15/7

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3(x+5i)=7yi-6+8

3 (x + 5 i) = 7 y i - 6 + 8

x = \frac{2}{3}, y = \frac{15}{7}

Solution steps

3 (x + 5 i) = 7 y i - 6 + 8

Rewrite

3 (x + 5 i)

in standard complex form:

3 x + 15 i

3 x + 15 i = 7 y i - 6 + 8

Rewrite

7 y i - 6 + 8

in standard complex form:

2 + 7 y i

3 x + 15 i = 2 + 7 y i

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

[3 x = 2 15 = 7 y]

[3 x = 2 15 = 7 y] : x = \frac{2}{3}, y = \frac{15}{7}

x = \frac{2}{3}, y = \frac{15}{7}

x - 5 i + 2 = 4 - 3 i + y i

(x + y i) + (4 + 9 i) = 9 - 4 i

x - i y = 3 + 4 i

5 i - 6 x = (10 y) i + 2

x^{2} - 7 x + 9 y i = y^{2} i + 20 i - 12

What is the answer to 3(x+5i)=7yi-6+8 ?
The answer to 3(x+5i)=7yi-6+8 is x= 2/3 ,y= 15/7