Mathematics 10 — Exercise 1.3 · Q1 (iv)

Full question

Find the modulus of the following complex number.

Step-by-step solution

1. Read a, the real coordinate.

   $$a=\left(-1\right)\times \sqrt{2}$$

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

   $$b=\left(-1\right)\times \sqrt{3}$$

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

   $$\sqrt{{\left(\left(-1\right)\times \sqrt{2}\right)}^2+{\left(\left(-1\right)\times \sqrt{3}\right)}^2}$$

4. Square the real coordinate.

   $${\left(\left(-1\right)\times \sqrt{2}\right)}^2=2$$

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

   $${\left(\left(-1\right)\times \sqrt{3}\right)}^2=3$$

6. Add the two squared values.

   $$2+3=5$$

7. Take the nonnegative square root of this sum.

   $$\sqrt{5}=\sqrt{5}$$

Answer

The final answer is shown below.