What is the answer to (a+2i)(b-i)=3+i ?

The answer to (a+2i)(b-i)=3+i is

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(a+2i)(b-i)=3+i

(a + 2 i) (b - i) = 3 + i

(a = 1, b = 1 a = - 2, b = - \frac{1}{2})

Solution steps

(a + 2 i) (b - i) = 3 + i

Expand

(a + 2 i) (b - i) : (ab + 2) + i (- a + 2 b)

(ab + 2) + i (- a + 2 b) = 3 + i

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

[ab + 2 = 3 - a + 2 b = 1]

[ab + 2 = 3 - a + 2 b = 1] : (a = 1, b = 1 a = - 2, b = - \frac{1}{2})

(a = 1, b = 1 a = - 2, b = - \frac{1}{2})

\frac{z - i}{z} = z + i

x + i y = (3 x + 4 i) (1 + x - i y)

z^{2} = i (∣ z ∣^{2} - 4)

(2 - 3 i) x + (3 - 2 i) y = 14 + 8 i

y - in y = x^{2} + 1