What is the answer to 6(4+7i)^2+A(4+7i)+B=0 ?

The answer to 6(4+7i)^2+A(4+7i)+B=0 is A=-48,B=390

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6(4+7i)^2+A(4+7i)+B=0

6 (4 + 7 i)^{2} + A (4 + 7 i) + B = 0

A = - 48, B = 390

Solution steps

6 (4 + 7 i)^{2} + A (4 + 7 i) + B = 0

Expand

6 (4 + 7 i)^{2} + A (4 + 7 i) + B : (- 198 + 4 A + B) + i (336 + 7 A)

(- 198 + 4 A + B) + i (336 + 7 A) = 0

Rewrite

0

in standard complex form:

0 + 0 i

(- 198 + 4 A + B) + i (336 + 7 A) = 0 + 0 i

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

[- 198 + 4 A + B = 0 336 + 7 A = 0]

[- 198 + 4 A + B = 0 336 + 7 A = 0] : A = - 48, B = 390

A = - 48, B = 390

x + i y = 1, 1 x + y = 1 + i

3 x^{2} - 125 i x - 3500 = 121 i x + 1543

a - bi = - b + ia

a - bi - 6 ai - 6 b i^{2} = 5 + 5 i

4 (3 + 6 i)^{2} + a (3 + 6 i) + b = 0

What is the answer to 6(4+7i)^2+A(4+7i)+B=0 ?
The answer to 6(4+7i)^2+A(4+7i)+B=0 is A=-48,B=390