Mathematics 10 — Exercise Worked examples · Example 4 (ii)

Full question

Evaluate the expression.

Step-by-step solution

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

   $$-(3\times i-4)-(2-5\times i)$$

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

   $$\left(-1\right)\times 2=-2$$

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

   $$\left(-1\right)\times \left(-5\right)=5$$

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

   $$4-3\times i-2+5\times i$$

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

   $$4-2+i\times \left(-3+5\right)$$

6. Calculate the real part only.

   $$4-2=2$$

7. Calculate the imaginary coefficient only.

   $$-3+5=2$$

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

   $$2\times i+2$$

Answer

The final answer is shown below.