September 14, 2015
Solve by completing the square (leave answer in simplest radical
form).
x2 + 6x - 4 = 0
Solution:
+
x = √13 - 3
September 14, 2015
P.6
Complex Numbers
Objective: Simplify expressions and solve equations with complex numbers.
Why: Complex numbers are used in fluid dynamics to determine
potential flow in two-dimensions; also with electrical impedance
with voltages and currents.
Solve:
x2 + 1 = 0
September 14, 2015
Objective: Simplify expressions and solve equations with complex numbers.
Complex Number:
a + bi
real part
imaginary part
Examples.
1. (2-i) + (3-√-3)
2. (5i - 3)(2i + 2)
3. (√-4 + i)(6 - 5i)
September 14, 2015
Try this:
(2 + 3i)(5 - i)
Put answer in standard form.
September 14, 2015
Objective: Simplify expressions and solve equations with complex numbers.
4. Find the real numbers x and y that make the equation true.
(x + 6i) = (3 - i) + (4 - 2yi)
September 14, 2015
Objective: Simplify expressions and solve equations with complex numbers.
5. If z = √3 + 1
i
2
2
find z3.
September 14, 2015
Objective: Simplify expressions and solve equations with complex numbers.
Complex Conjugates:
The complex conjugate of the complex number z = a + bi is
z = a + bi = a - bi
To simplify a quotient of 2 complex numbers, multiply the
numerator and denominator by the complex conjugate of the
denominator.
Simplify.
1.
2.
i
2-i
2-i
2+i
September 14, 2015
Try this:
Simplify. Put in standard form.
2
3-i
September 14, 2015
Objective: Simplify expressions and solve equations with complex numbers.
Solve the equation using the quadratic formula.
3x2 + x + 2 = 0
September 14, 2015
(P.6) Pg. 52: 3-11odd, 25-29odd, 35, 36, 41, 43