Mathematics 10 — Exercise 1.3 · Q1 (i)

Full question

Find the modulus of the following complex number.

Step-by-step solution

1. Read a, the real coordinate.

   $$a=4$$

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

   $$b=3$$

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

   $$\sqrt{4^2+3^2}$$

4. Square the real coordinate.

   $$4^2=16$$

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

   $$3^2=9$$

6. Add the two squared values.

   $$16+9=25$$

7. Take the nonnegative square root of this sum.

   $$\sqrt{25}=5$$

Answer

The final answer is shown below.