What is the answer to (a+2i)(b-1)=3+i ?

The answer to (a+2i)(b-1)=3+i is a=6,b= 3/2

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(a+2i)(b-1)=3+i

(a + 2 i) (b - 1) = 3 + i

a = 6, b = \frac{3}{2}

Solution steps

(a + 2 i) (b - 1) = 3 + i

Rewrite

(a + 2 i) (b - 1)

in standard complex form:

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

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

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

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

[ab - a = 3 2 b - 2 = 1] : a = 6, b = \frac{3}{2}

a = 6, b = \frac{3}{2}

z^{2} = 3 i

i = z^{2}

(x - y i)^{2} = 3 - 4 i

i x^{2} - 2 x + i = 0

\frac{6}{x + y i} + (2 - i)^{2} = 4 - 3 i

What is the answer to (a+2i)(b-1)=3+i ?
The answer to (a+2i)(b-1)=3+i is a=6,b= 3/2