Transcript imaginary-numbers-eoct-review-with

Imaginary Numbers Review
Imaginary Numbers
Quadratic Forms
Converting Standard Form
Imaginary Numbers
Remember, when we take the square root of a negative number, we need
to use i.
i  1
The pattern for powers of i looks like this:
i  1
i 2  1
i  i
3
i4  1
Complex Numbers
Standard form:
a  bi
Algebraically, we can treat i just like a variable (we can add, subtract, multiply
and divide it)
To add or subtract, just combine your like terms
(4  3i )  (2  2i )  4  2  3i  2i  2  5i
To multiply, use the distributive property and remember that i^2 = -1!
2
(4  3i)( 2  2i)  8  8i  6i  6i  14  2i
To divide, we can’t have an imaginary number in the denominator, so we must
use the complex conjugate.
4  3i 2  2i 8  8i  6i  6i
2  14i
4  3i




2
8
2  2i 2  2i 2  2i 4  4i  4i  4i
2
Quadratics
Standard form:
Vertex form:
y  ax  bx  c
2
y  a ( x  h)  k
Intercept Form:
2
y  a( x  p)( x  q)
Quadratic Formula:
 b  b 2  4ac
2a
Axis of Symmetry:
b
2a
Converting to Vertex Form
• Use ‘completing the
square’ method.
x  6x  4  0
2
( x  6x  9 )  4  0  9
2
Divide ‘b’ by 2 and square to find the ‘new c’
( x  3) 2  4  9
( x  3) 2  5  0
Practice Questions: