What is the answer to p(2i+6j)+q(2i-4j)=6i-7j ?

The answer to p(2i+6j)+q(2i-4j)=6i-7j is p= 1/2 ,q= 5/2 ,\quad j\ne 0

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p(2i+6j)+q(2i-4j)=6i-7j

p (2 i + 6 j) + q (2 i - 4 j) = 6 i - 7 j

p = \frac{1}{2}, q = \frac{5}{2}, j \neq = 0

Solution steps

p (2 i + 6 j) + q (2 i - 4 j) = 6 i - 7 j

Rewrite

p (2 i + 6 j) + q (2 i - 4 j)

in standard complex form:

(6 j p - 4 j q) + (2 p + 2 q) i

(6 j p - 4 j q) + (2 p + 2 q) i = 6 i - 7 j

Rewrite

6 i - 7 j

in standard complex form:

- 7 j + 6 i

(6 j p - 4 j q) + (2 p + 2 q) i = - 7 j + 6 i

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

[6 j p - 4 j q = - 7 j 2 p + 2 q = 6]

[6 j p - 4 j q = - 7 j 2 p + 2 q = 6] : p = \frac{1}{2}, q = \frac{5}{2}, j \neq = 0

p = \frac{1}{2}, q = \frac{5}{2}, j \neq = 0

(3 + i) x^{2} + 10 x - (9 + 3 i) = 0

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

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

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

2 x - 4 y i = 10 - 5 i

What is the answer to p(2i+6j)+q(2i-4j)=6i-7j ?
The answer to p(2i+6j)+q(2i-4j)=6i-7j is p= 1/2 ,q= 5/2 ,\quad j\ne 0