Could someone me with a few Algebra 2 problems?

In summary: So the final answer would be 5x^5y^7.5 over 325.In summary, the conversation discusses solving problems involving imaginary numbers and radicals. Various problems are mentioned, including simplifying expressions, solving equations, and using properties of exponents. The steps for solving each problem are outlined and explained.
  • #1
Timberizer
4
0
I'm learning about imaginary numbers and radicals.

Here are the ones I need help with. Could someone explain how to do them, and what the answers are? Thanks

1. 2X + Yi = 3X + 1 + 3i (solve for X and Y)

2. (-4-5i)^2 (solve in a+bi form)

3. (1 - 2i)(-5 + 6i) (simplify in a +bi form)

4.
_____ _____
\/-32 + \/-50

5.

3___ 6_____
\/4 * \/3

6.

_______
\/ X + 7 = X-13 (solve for X if possible)

7.

5_________
/ X^10 Y^15
/_________
\/ 32

8.
________ ________
\/ 3X + 4 = \/ 2X + 3
 
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  • #2
1. The real parts are equal, the imaginary parts are equal.
2. Just foil it like you normally would, then when your done simplify your i's
3. Same thing as 2.
4. Write 32 and 50 out as products of their primes, ( 32 = 2*2*2*2*2), then take pairs of primes (2*2=4) and isolate them ([itex]\sqrt{32} = \sqrt{(2)(2)(2)(2)(2)} = \sqrt{(4)(2)(2)(2)} = 2\sqrt{(2)(2)(2)} [/itex]. Repeat until it is as simple as possible (you will be left with one term inside). From here, just use the definition of i to simplify the last bit. Do the same for 50.

[tex] 5. \frac{(3)(6)}{\sqrt{4}\sqrt{3}} [/tex] ? This ones easy, the denominator simplifies right away, no complex numbers involved. Dont forget to rationalize.

6. Square both sides
7. No idea what htis says
8. Square both sides
 
  • #3
5.[tex] \frac{(3)(6)}{\sqrt{4}\sqrt{3}} [/tex] ? This ones easy, the denominator simplifies right away, no complex numbers involved. Dont forget to rationalize.

Thanks for the help, but you mixed up that problem. It was actually 3 root 4 times 6 root 3
 
Last edited by a moderator:
  • #4
#7 is actually: 5 root X^10 Y^15 over 32
 
  • #5
5: 3rd root of 4? As in 4^(1/3) ? or 3 times square root of 4?

7: A square root can be expressed as ^(1/2), for example, square root of x^10 = (x^10)^(1/2). By properties of exponents this simplifies to x^5. Apply this to the rest.
 

Related to Could someone me with a few Algebra 2 problems?

1. How do I solve equations with variables on both sides?

To solve equations with variables on both sides, you need to first combine like terms on each side of the equation. Then, isolate the variable on one side by using inverse operations. Finally, solve for the variable by simplifying the equation.

2. What is the difference between an expression and an equation?

An expression is a mathematical phrase that may contain variables, numbers, and operations, but does not have an equal sign. An equation, on the other hand, has an equal sign and shows that two expressions are equal.

3. How do I solve systems of equations?

To solve systems of equations, you can use substitution or elimination. Substitution involves solving for one variable in one equation and plugging it into the other equation. Elimination involves adding or subtracting the equations to eliminate one variable. The resulting equation can then be solved to find the value of the remaining variable.

4. What is the difference between a function and an equation?

A function is a rule that assigns each input a unique output. It can be represented by an equation, but it does not always have to be. An equation, on the other hand, shows the relationship between two or more variables and is often used to solve for the value of a variable.

5. How do I graph quadratic equations?

To graph a quadratic equation, you can use the vertex form or the standard form. The vertex form is y = a(x-h)^2 + k, where (h,k) is the vertex of the parabola. The standard form is y = ax^2 + bx + c, where a, b, and c determine the shape and position of the parabola. You can also use the quadratic formula to find the x-intercepts of the graph.

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