Solving Complex Roots: x^2 + 25 = 0

[Corkery]

[SOLVED] Compex roots

Homework Statement

state the number of complex roots of each equation, then find the roots and graph the related function.

x^2 + 25 = 0

Homework Equations

The Attempt at a Solution

x^2 + 25 = 0

so there are 2 complex roots. Once I have established that then I minus the 25 to the other side.

x^2 = -25

square root both sides.

x = +/-5i

I'm pretty sure everything up to this point is correct but the thing I did above I think it is wrong. Firstly because if there are two complex roots and I already have one of them what is the other one. I'm confused, so please help me. thank you.

 

[rock.freak667]

you have both roots...x=+5i and x=-5i ...it is correct

 

[Architeuthis Dux]

I can confirm that your solution is correct. The equation x^2 + 25 = 0 has two complex roots, which are +/-5i. This means that when you plug in either of these values for x, the equation will equal 0.

The reason you are confused about what the other root is can be explained by the fundamental theorem of algebra, which states that a polynomial equation of degree n will have exactly n complex roots. In this case, the equation has a degree of 2, so it will have two complex roots. However, these roots may not always be easy to determine or express in a simple form. In this case, one of the roots is 5i, which is a simple and easy to understand form, but the other root may not have a simple form. This is why we often use the +/- sign to represent both roots.

To graph the related function, you can plot the points (0, 5i) and (0, -5i) on a complex plane, which is similar to a normal Cartesian plane but with the real and imaginary axes. This will give you two points on a straight line parallel to the imaginary axis. You can then plot more points to get a better understanding of the shape of the function.

Overall, your solution is correct and your confusion is understandable. Complex roots can be tricky to understand and work with, but with practice and understanding of the fundamental theorem of algebra, you can become more comfortable with them.