We want to plot the given complex number and find its absolute value.

2 i

Let's start with the graph. Then, we can use our graph to calculate the absolute value.

Graphing the Complex Number

In the complex number plane, the point

(a, b)

represents the complex number

a + b i .

To graph a complex number, we need to locate the real part on the horizontal axis and the imaginary part on the vertical axis. Let's identify the real and imaginary parts of the given number.

2 i \Leftrightarrow 0 + 2 i

For the given number, the real part is

0

and the imaginary part is

2 .

Finding the Absolute Value

The absolute value of a complex number is defined as its distance from the origin

(0, 0)

in the complex plane. It is represented above by the

diagonal

segment .

To calculate the absolute value, we use a modified version of the Distance Formula.

∣ a + b i ∣ = a^{2} + b^{2}

In this formula, we will substitute

0

and

2

for

a

and

b,

respectively.

∣ a + b i ∣ = a^{2} + b^{2}

SubstituteII

$a = 0$ , $b = 2$

∣ 0 + (2) i ∣ = 0^{2} + (2)^{2}

▼

Simplify

CalcPow

Calculate power

∣ 2 i ∣ = 0 + 4

AddTerms

Add terms

∣ 2 i ∣ = 4

CalcRoot

Calculate root

∣ 2 i ∣ = 2

The absolute value of the complex number

2 i

is

2 .

Exercise 13 Page 253

Hints

Check the answer

Practice exercises

Asses your skill

Graphing the Complex Number

Finding the Absolute Value