(5+2i)^2-10(5+2i)=-29

2 min read Jun 16, 2024

Solving the Equation: (5+2i)^2 - 10(5+2i) = -29

This equation involves complex numbers, and we can solve it by simplifying the left-hand side and then isolating the variable. Let's break down the steps:

1. Expanding the Square

First, we expand the square term:

(5+2i)^2 = (5+2i)(5+2i) = 25 + 10i + 10i + 4i^2

Remember that i^2 = -1, so we can substitute:

25 + 10i + 10i + 4i^2 = 25 + 20i - 4 = 21 + 20i

2. Distributing the Multiplication

Now, we distribute the -10:

-10(5+2i) = -50 - 20i

3. Combining Terms

Substitute the expanded terms back into the original equation:

(21 + 20i) + (-50 - 20i) = -29

Simplifying the left side:

-29 = -29

Conclusion

The equation is true, which means that (5+2i) is a solution to the equation.

In conclusion, the given equation is an identity, meaning it is true for any value of the complex number (5+2i). This is because the left-hand side simplifies to -29, which is equal to the right-hand side.