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

The answer to 2i=ix(2-3i)-y(5-3i) is x= 10/19 ,y= 6/19

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2i=ix(2-3i)-y(5-3i)

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

x = \frac{10}{19}, y = \frac{6}{19}

Solution steps

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

Expand

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

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

Rewrite

2 i

in standard complex form:

0 + 2 i

0 + 2 i = (3 x - 5 y) + i (2 x + 3 y)

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

[0 = 3 x - 5 y 2 = 2 x + 3 y]

[0 = 3 x - 5 y 2 = 2 x + 3 y] : x = \frac{10}{19}, y = \frac{6}{19}

x = \frac{10}{19}, y = \frac{6}{19}

(5 + 6 i) (x + y i) = 60 + 11 i

x, c u a d r a t i c a = x^{2} + 4

r, i = \frac{e}{r}

x + y i = 3 - 2 i

Z^{2} = 3 - 4 i

What is the answer to 2i=ix(2-3i)-y(5-3i) ?
The answer to 2i=ix(2-3i)-y(5-3i) is x= 10/19 ,y= 6/19