Respuesta :
Well, the first step would be to multiply everything out. 1*2=2, g1*i=i, g2i*2=4i, and 2i*i=2i^2. This would bring the equation to 2+i+4i+2i^2=5(2+i)
Next, multiply the other side. 5*2=10, and 5*i=5i. The equation is now:
2+i+4i+2i^2=10+5i
Now, combine like terms, and arrange the sides from highest exponents to lowest exponents: i+4i=5i. You can arrange the equation to 2i^2+5i+2=5i+10.
Subtract 2 from both sides: 2i^2+5i=5i+8
Subtract 5i from both sides: 2i^2=8
Divide both sides by 2: i^2=4.
Finally, find the square root of 4 to get i. The square root of 4 is 2, so i=2.
The missing term in the complex equation (1 + 2i)(2 + i) + x = 5(2 + i) will be 9.
What is the solution of the equation?
The solution of the equation means the value of the unknown or variable.
The complex number is the combination of the real part and the imaginary part. Then the complex number is given as a + bi.
Let x be the missing term. Then the equation will be
(1 + 2i)(2 + i) + x = 5(2 + i)
Simplify the equation, then the complex equation will be
1(2 + i) + 2i(2 + i) + x = 5(2 + i)
2 + i + 4i + i² + x = 10 + 5i
We know that i² = -1, then the equation will be
2 + i + 4i – 1 + x = 10 + 5i
x + 5i + 1 = 10 + 5i
Subtract 5i from both sides, then the equation will be
x + 1 = 10
x = 10 – 1
x = 9
The missing term in the complex equation (1 + 2i)(2 + i) + x = 5(2 + i) will be 9.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
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