Mathematics 10 — Exercise Worked examples · Example 7

Full question

For z = −7 − 4i, show z + 0 = z.

Step-by-step solution

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

   $$-(4\times i+7)+0$$

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

   $$-7-4\times i+0+0\times i$$

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

   $$-7+0+i\times \left(-4+0\right)$$

4. Calculate the real part only.

   $$-7+0=-7$$

5. Calculate the imaginary coefficient only.

   $$-4+0=-4$$

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

   $$-4\times i-7$$

Answer

The final answer is shown below.