What is the answer to a+b-2abi=5-12i ?

The answer to a+b-2abi=5-12i is

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a+b-2abi=5-12i

a + b - 2 abi = 5 - 12 i

(a = 2, b = 3 a = 3, b = 2)

Solution steps

a + b - 2 abi = 5 - 12 i

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

[a + b = 5 - 2 ab = - 12]

[a + b = 5 - 2 ab = - 12] : (a = 2, b = 3 a = 3, b = 2)

(a = 2, b = 3 a = 3, b = 2)

x^{2} + (1 - i) x + (2 - 2 i) = 0

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

\frac{a + 7 i}{3 - 2 i} = 1 + bi

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

a - bi - 1 = \frac{15 + 8 i}{4 ( a + bi )}