Mathematics 10 — Exercise 1.3 · Q1 (ii)

Full question

Find the modulus of the following complex number.

Step-by-step solution

1. Read a, the real coordinate.

   $$a=-5$$

2. Read b, the coefficient of i, including its sign.

   $$b=-4$$

3. Use |z| = √(a² + b²) and substitute both coordinates.

   $$\sqrt{{\left(-5\right)}^2+{\left(-4\right)}^2}$$

4. Square the real coordinate.

   $${\left(-5\right)}^2=25$$

5. Square the imaginary coordinate; a negative number squared is positive.

   $${\left(-4\right)}^2=16$$

6. Add the two squared values.

   $$25+16=41$$

7. Take the nonnegative square root of this sum.

   $$\sqrt{41}=\sqrt{41}$$

Answer

The final answer is shown below.