What is the answer to 5(a+bi)+i(a+bi)+4=0 ?

The answer to 5(a+bi)+i(a+bi)+4=0 is a=-10/13 ,b= 2/13

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5(a+bi)+i(a+bi)+4=0

5 (a + bi) + i (a + bi) + 4 = 0

a = - \frac{10}{13}, b = \frac{2}{13}

Solution steps

5 (a + bi) + i (a + bi) + 4 = 0

Expand

5 (a + bi) + i (a + bi) + 4 : (5 a - b + 4) + i (a + 5 b)

(5 a - b + 4) + i (a + 5 b) = 0

Rewrite

0

in standard complex form:

0 + 0 i

(5 a - b + 4) + i (a + 5 b) = 0 + 0 i

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

[5 a - b + 4 = 0 a + 5 b = 0]

[5 a - b + 4 = 0 a + 5 b = 0] : a = - \frac{10}{13}, b = \frac{2}{13}

a = - \frac{10}{13}, b = \frac{2}{13}

\frac{a}{h} = \frac{- i}{d}

(a + bi) (x - y i) = 2 + 2 i

i x^{2} - 2 x - 2 i = 0

(a + ib)^{2} + 2 (a - ib) + 6 = 0

z^{2} - z (1 + 4 i) + 12 i - 6 = 0

What is the answer to 5(a+bi)+i(a+bi)+4=0 ?
The answer to 5(a+bi)+i(a+bi)+4=0 is a=-10/13 ,b= 2/13