What is the answer to (a+7i)/(3-2i)=1+bi ?

The answer to (a+7i)/(3-2i)=1+bi is a=9,b=3

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(a+7i)/(3-2i)=1+bi

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

a = 9, b = 3

Solution steps

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

Multiply both sides by

3 - 2 i

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

Simplify

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

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

[a = 3 + 2 b 7 = - 2 + 3 b]

[a = 3 + 2 b 7 = - 2 + 3 b] : a = 9, b = 3

a = 9, b = 3

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

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

(a + bi)^{2} = 2 i

\frac{2 i z}{1 + i} = \frac{i}{- z}

x + i y = 1

What is the answer to (a+7i)/(3-2i)=1+bi ?
The answer to (a+7i)/(3-2i)=1+bi is a=9,b=3