Quadratic Formula with Imaginary Numbers

Quadratic Formula and Imaginary Numbers

Part 2

WARM UP

SOLVING QUADRATICS

So far, to solve a quadratic we have the method of _________________.
However, there will be times when factoring does not work, in which case
we resort to a different method.

Recall: A quadratic can have 0 real solutions. When this is the case, we call
our solutions __________________.

We have to understand what imaginary numbers are before using methods
that involve imaginary solutions.

factoring

imaginary solutions

START THINKING…

=

=

IMAGINARY NUMBERS

i

i

-1

i

EXAMPLES

COMPLEX NUMBERS

How can you add and subtract complex numbers? ___________________
the _________________parts and ___________________ parts of the
complex number as you would combine like terms.

Examples

What is the sum of (4 – 7i) and (-11 + 9i)?

What is the difference of (8 + 6i) and (2 – 5i)? Remember to ___________
the _____________.

COMBINING COMPLEX NUMBERS

4 - 7i + (-11 + 9i)
4 - 7i -11 + 9i = - 7+ 2i

8 + 6i - (2 - 5i)
8 + 6i -2 + 5i = 6 +11i

YOU TRY!

Explore and reason

quizizz

interactive

Multiple Choice

Simplify √-4

• 2i
• -2i
• 2
• 4i

Multiple Choice

Simplify √-81

• -√81
• -9i
• 9i
• 81i

Multiple Choice

Desean begins to use the quadratic formula to solve the following equation.

$$x^2-3x=9$$  

Which expression shows a step in solving the above equation?

• $$\frac{3\pm\sqrt{45}}{2}$$  

• $$\frac{-3\pm\sqrt{45}}{2}$$  

• $$\frac{3\pm\sqrt{-27}}{2}$$  

• $$\frac{-3\pm\sqrt{-27}}{2}$$  

Multiple Choice

$$x^2-6x+34$$  
What are the roots of the equation in a+bi form?

• $$3+5i$$  

• $$3\pm5i^{ }$$  

• $$6\pm10i$$  

Multiple Choice

$$x^2-16x+80=0$$  
What are the roots of the equation in a+bi form.

• $$16\pm8i$$  

• $$16\pm8$$  

• $$8\pm4i$$  

• $$8\pm4$$