What is the answer to (a-6i)/(-2+3i)=b-7 ?

The answer to (a-6i)/(-2+3i)=b-7 is a=4,b=5

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(a-6i)/(-2+3i)=b-7

\frac{a - 6 i}{- 2 + 3 i} = b - 7

a = 4, b = 5

Solution steps

\frac{a - 6 i}{- 2 + 3 i} = b - 7

Multiply both sides by

- 2 + 3 i

\frac{a - 6 i}{- 2 + 3 i} (- 2 + 3 i) = b (- 2 + 3 i) - 7 (- 2 + 3 i)

Expand

a - 6 i = (- 2 b + 14) + i (- 21 + 3 b)

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

[a = - 2 b + 14 - 6 = - 21 + 3 b]

[a = - 2 b + 14 - 6 = - 21 + 3 b] : a = 4, b = 5

a = 4, b = 5

x, x^{2} + 2 x i - 5 = 3 i

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

∣ z - 2 i ∣ = 4

1 + 3 i e z^{2} = (1 - i)

x + (y - 2) i = 3

What is the answer to (a-6i)/(-2+3i)=b-7 ?
The answer to (a-6i)/(-2+3i)=b-7 is a=4,b=5