What is the answer to (x+2i)/(1-i)+yi=1 ?

The answer to (x+2i)/(1-i)+yi=1 is x=4,y=-3

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(x+2i)/(1-i)+yi=1

\frac{x + 2 i}{1 - i} + y i = 1

x = 4, y = - 3

Solution steps

\frac{x + 2 i}{1 - i} + y i = 1

Multiply both sides by

1 - i

\frac{x + 2 i}{1 - i} (1 - i) + y i (1 - i) = 1 \cdot (1 - i)

Simplify

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

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

[x + y = 1 2 + y = - 1]

[x + y = 1 2 + y = - 1] : x = 4, y = - 3

x = 4, y = - 3

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

x, x sin (y) - x^{2} y^{- 3} = c

z^{2} = - 3 - 4 i

(a + 6) + 2 bi = 6 - 5 i

(\frac{1 - i}{1 + i})^{100} = a + ib

What is the answer to (x+2i)/(1-i)+yi=1 ?
The answer to (x+2i)/(1-i)+yi=1 is x=4,y=-3