Mathematics 10 — Exercise 1.2 · Q1 (ii)

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.

   $$-(3\times i-16)+2\times i+9$$

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

   $$16-3\times i+9+2\times i$$

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

   $$16+9+i\times \left(-3+2\right)$$

4. Calculate the real part only.

   $$16+9=25$$

5. Calculate the imaginary coefficient only.

   $$-3+2=-1$$

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

   $$25-i$$

Answer

The final answer is shown below.