Jasonbradley
Home

(z+5i)(4+2i)-(z+2)(4+2i)=24+2i

2 min read Jun 17, 2024
(z+5i)(4+2i)-(z+2)(4+2i)=24+2i

Solving the Complex Equation: (z+5i)(4+2i)-(z+2)(4+2i)=24+2i

This article will guide you through the steps to solve the complex equation: (z+5i)(4+2i)-(z+2)(4+2i)=24+2i.

Let's break it down:

Simplifying the Equation

  1. Distribute: Expand the products on both sides of the equation:

    • (z+5i)(4+2i) = 4z + 2zi + 20i - 10
    • (z+2)(4+2i) = 4z + 2zi + 8 + 4i

  2. Substitute: Substitute the expanded products back into the original equation:

    • (4z + 2zi + 20i - 10) - (4z + 2zi + 8 + 4i) = 24 + 2i

  3. Simplify: Combine like terms:

    • 16i - 18 = 24 + 2i

Solving for z

  1. Isolate i terms: Subtract 2i from both sides and add 18 to both sides:

    • 14i = 42

  2. Solve for i: Divide both sides by 14:

    • i = 3

  3. Substitute i back: Since we know i = 3, there is no 'z' term in the equation, meaning there is no solution for 'z'.

Conclusion:

The equation (z+5i)(4+2i)-(z+2)(4+2i)=24+2i has no solution for 'z'. This is because the equation simplifies to an equation with only 'i' terms, and there is no 'z' term to solve for.

Related Post

Featured Posts