https://file.aiquickdraw.com/mathbot/file/1725444166968u1qvv689.jpg

Can you carefully type me these questions?

Here are the questions typed out:

---

**Q.2 Give Short Answers to following Questions:**

(i) Express the \(0.59\) recurring decimal as the rational number \(\frac{p}{q}\), where \(p, q\) are integers and \(q \neq 0\).

(ii) Represent on number line: \(-\frac{1}{3}\).

(iii) Use law of exponents to simplify: 
\[
\left(\frac{x^2 y^{-3}}{x^{-1} y^4}\right)^3
\]

(iv) Simplify:
\[
\frac{4(3)^3}{3\sqrt{2}}
\]

(v) Separate real and imaginary parts of: \( (1 + \sqrt{-2})^2 \).

---

**Q.3 Answer the following Questions:**

(a) Simplify that: 
\[
\frac{(81)^{\frac{1}{4}} \times 3^2 - 4(3\sqrt{243})}{6\sqrt{3} \times (3)^2}
\]

(b) Solve the equation \( 3(x+4i)^2 - 2(x - yi) = x + yi \) for real \(x\) and \(y\).

---

Would you like further details or explanations for any of these questions? Here are some follow-up questions:

1. What method do you prefer to solve the equation in Q3(b)?
2. Would you like to review how to represent numbers on the number line as in Q2(ii)?
3. Are you familiar with the laws of exponents used in Q2(iii)?
4. Do you need clarification on simplifying complex expressions like in Q2(iv)?
5. How comfortable are you with separating real and imaginary parts as in Q2(v)?

**Tip:** When simplifying expressions with exponents, remember to apply the rules of exponents step-by-step to avoid errors.

Explore solutions to various mathematical problems involving rational numbers, number line representation, laws of exponents, simplification of expressions, and separation of real and imaginary parts in complex numbers. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation