Question

Find a complex number z that satisfies the following equation:
(4+2i)⋅z = 5+2i−2z

Answer 1

To find a complex number that satisfies the given equation, multiply both sides of the equation by the complex number (4+2i), distribute and combine like terms, then solve for z by isolating it on one side of the equation.

Step-by-step explanation:

To find a complex number that satisfies the given equation, (4+2i)⋅z = 5+2i−2z, we can write it in the form az = b, where a = 4+2i and b = 5+2i−2z. Then we can solve for z. Here are the steps:

1. Distribute the left side: (4+2i)⋅z = 4z+2iz
2. Combine like terms on the right side: b = 5+2i−2z
3. Move -2z to the left side: 4z + 2iz + 2z = 5+2i
4. Combine like terms: 6z + 2iz = 5+2i
5. Factor out z: z(6+2i) = 5+2i
6. Divide both sides by (6+2i): z = (5+2i)/(6+2i)

Therefore, the complex number z that satisfies the equation is (5+2i)/(6+2i).