What is the answer to (1+5i)p-2q=3+7i ?

The answer to (1+5i)p-2q=3+7i is p= 7/5 ,q=-4/5

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(1+5i)p-2q=3+7i

(1 + 5 i) p - 2 q = 3 + 7 i

p = \frac{7}{5}, q = - \frac{4}{5}

Solution steps

(1 + 5 i) p - 2 q = 3 + 7 i

Rewrite

(1 + 5 i) p - 2 q

in standard complex form:

(p - 2 q) + 5 p i

(p - 2 q) + 5 p i = 3 + 7 i

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

[p - 2 q = 3 5 p = 7]

[p - 2 q = 3 5 p = 7] : p = \frac{7}{5}, q = - \frac{4}{5}

p = \frac{7}{5}, q = - \frac{4}{5}

x + y i = 3 - 2 i

(x + i y)^{2} - 3 i (x + i y) - 2 = 0

2 + i y = x - 2 i

\frac{6}{x + y i + ( 2 - i ) ^{2}} = 4 - 3 i

∣ z - i ∣ = 2 z + i

What is the answer to (1+5i)p-2q=3+7i ?
The answer to (1+5i)p-2q=3+7i is p= 7/5 ,q=-4/5