Mathematics 10 — Exercise 1.1 · Q3 (v)

Full question

Find the real values of x and y that satisfy the following equality of complex numbers.

Step-by-step solution

1. Expand the brackets and replace i² by −1.

   $$2\times i\times y-3\times i+3\times x-1=7\times i+8$$

2. Equal complex numbers have equal real parts and equal coefficients of i. Match these separately.

   $$(3\times x-1=8,2\times y-3=7)$$

3. Use the equation containing only the first variable.

   $$3\times x-1=8$$

4. Subtract the constant term from both sides.

   $$3\times x-1+1=8+1$$

5. Simplify the subtraction.

   $$3\times x=9$$

6. Divide both sides by the coefficient.

   $$x=\frac{9}{3}$$

7. Simplify the fraction.

   $$x=3$$

8. Use the other original equation to find the second variable.

   $$2\times y-3=7$$

9. Subtract the constant from both sides.

   $$2\times y-3+3=7+3$$

10. Simplify the two sides.

    $$2\times y=10$$

11. Divide both sides by the coefficient.

    $$y=\frac{10}{2}$$

12. Simplify to find the second value.

    $$y=5$$

13. Check both values in the original complex equation.

    $$7\times i+8=7\times i+8$$

Answer

The final answer is shown below.