What is the answer to (a+4i)(c+4i)=2+36i ?

The answer to (a+4i)(c+4i)=2+36i is

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(a+4i)(c+4i)=2+36i

(a + 4 i) (c + 4 i) = 2 + 36 i

(a = 3, c = 6 a = 6, c = 3)

Solution steps

(a + 4 i) (c + 4 i) = 2 + 36 i

Expand

(a + 4 i) (c + 4 i) : (a c - 16) + i (4 a + 4 c)

(a c - 16) + i (4 a + 4 c) = 2 + 36 i

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

[a c - 16 = 2 4 a + 4 c = 36]

[a c - 16 = 2 4 a + 4 c = 36] : (a = 3, c = 6 a = 6, c = 3)

(a = 3, c = 6 a = 6, c = 3)

z^{2} + 3 - i = 0

\frac{a + 2 i}{3 + bi} = 4 - 3 i

2 y - 3 + (4 x + 8) i = 0

i (x + y i) = (1 - 6 i) (2 + 3 i)

(a - 2 i)^{2} = 21 - 20 i