What is the answer to 2i(a+bi)+6=9i+(a+bi) ?

The answer to 2i(a+bi)+6=9i+(a+bi) is a= 24/5 ,b= 3/5

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2i(a+bi)+6=9i+(a+bi)

2 i (a + bi) + 6 = 9 i + (a + bi)

a = \frac{24}{5}, b = \frac{3}{5}

Solution steps

2 i (a + bi) + 6 = 9 i + (a + bi)

Simplify

(- 2 b + 6) + 2 ia = a + i (9 + b)

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

[- 2 b + 6 = a 2 a = 9 + b]

[- 2 b + 6 = a 2 a = 9 + b] : a = \frac{24}{5}, b = \frac{3}{5}

a = \frac{24}{5}, b = \frac{3}{5}

(x + i y)^{2} = 3 + 2 i

(9 - 7 i) - 7 = x - (7 + y i)

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

\frac{z}{z + i} = 4

i (x - i y) = - i (x - i y)

What is the answer to 2i(a+bi)+6=9i+(a+bi) ?
The answer to 2i(a+bi)+6=9i+(a+bi) is a= 24/5 ,b= 3/5