What is the answer to (2+5i)/(1-i)=x+yi ?

The answer to (2+5i)/(1-i)=x+yi is x=-3/2 ,y= 7/2

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(2+5i)/(1-i)=x+yi

\frac{2 + 5 i}{1 - i} = x + y i

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

Solution steps

\frac{2 + 5 i}{1 - i} = x + y i

Expand

\frac{2 + 5 i}{1 - i} : - \frac{3}{2} + \frac{7 i}{2}

- \frac{3}{2} + \frac{7 i}{2} = x + y i

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

[- \frac{3}{2} = x \frac{7}{2} = y]

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

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

a, ∣ a + bi ∣ = 1

a, ∣ a + bi ∣ = 3

i (x) = x^{2} + 4 x + 7

z = 2 e^{i (\frac{π}{3})}

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

What is the answer to (2+5i)/(1-i)=x+yi ?
The answer to (2+5i)/(1-i)=x+yi is x=-3/2 ,y= 7/2