Mathematics 10 — Exercise 1.2 · Q1 (iv)

Full question

Simplify the following expression and express the result in the standard form a + bi, where a and b are real numbers.

Step-by-step solution

1. Write both complex numbers with their real and imaginary parts.

   $$9\times i+11-(9-7\times i)$$

2. Multiply the real term of the second bracket by −1.

   $$\left(-1\right)\times 9=-9$$

3. Multiply its imaginary coefficient by −1 as well.

   $$\left(-1\right)\times \left(-7\right)=7$$

4. Remove the brackets, preserving the signs of all four terms.

   $$11+9\times i-9+7\times i$$

5. Place the real terms together. Factor i out of the imaginary terms.

   $$11-9+i\times \left(9+7\right)$$

6. Calculate the real part only.

   $$11-9=2$$

7. Calculate the imaginary coefficient only.

   $$9+7=16$$

8. Put these two results into a + bi form.

   $$16\times i+2$$

Answer

The final answer is shown below.