## Algebra 2 Tutorial

*Square Roots of Complex Numbers*

#### Intro

Just like for real numbers there will be two square roots for a complex number.

Finding these roots involves solving a system of two equations in two unknowns

Let’s say we want the square root of .

The square root will be of the form

Then

The minus sign in front of b squared comes from squaring i. Please notice that:

is also equal to

and so we have a second root

……..(the real part)

……………(the imaginary part)

#### Sample Problem

#### Solution

[eq 1] ……..(the real part)

[eq 2] ……………(the imaginary part)

Substitution

…………from the eq 2

…….substituting into eq1

[eq 3] multiplying by and collecting terms on left hand side

Factoring:

notice:

so by eq 3

a is the real part, so we can throw out a=i and

we are left with

and so

or (two roots).

We know that (eq2).

So if then .

THE ANSWER

check:

comes from

………….combining like terms

notice the second root is

comes from

………….combining like terms

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