Quadratic Formula with Imaginary Numbers

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!

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