ALGEBRA II HONORS/GIFTED - SECTION 4-8 (Complex Numbers)

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ALGEBRA II HONORS/GIFTED - SECTION 4-8 (Complex Numbers) @ SECTION 4-8 : COMPLEX NUMBERS

Solve the equation that corresponds to your group number. x2 = -100 m2 = -200 z2 + 12 = -8 11 – 5r2 = -49 100s2 + 600 = 400 5p2 – 12 = p2 – 13 -3(n + 5)2 = 9

We all know :

Find : Now, let’s re-visit those equations.

An imaginary number has an “i” in it. Complex Number : is in Standard Form, a + bi , where a and b are real numbers. Pure Imaginary numbers have a = 0. Complex Conjugate : The complex conjugate of a + bi is a – bi. Find the complex conjugate of each number. 13) 7 + 5i 14) 6 – 7i 15) -8 + 9i 16) -3 - i 17) 14i 18) 24

Graph each Complex Number. Use an Argand Diagram. Imaginary Axis 15) -4 – 3i 16) 3 – 4i 17) -6 + 2i 18) 5i Real Axis

Given z1 = 3 + 4i, z2 = 5 – 2i, and z3 = 10 + i, find 22) z1 + z2 23) z2 – z3 29) 24) 5 • z3 30) 25) i • z2 31) 26) z1 • z2 27) z3 • z2

i0 = 1 i4 = i2 • i2 = -1 • -1 = 1 i1 = i i5 = i4 • i = 1 • i = i i2 = -1 i6 = i5 • i = i • i = i2 = -1 i3 = i2 • i = -1 • i = -i i7 = i6 • i = -1 • i = -i MEMORIZE this chart : i0 = 1 i1 = i i2 = -1 i3 = -i

Simplify. 32) i237 33) i1492 34) i2018 35) i795 36) i1783451238946176238726 Remember : The divisibility test for 4 – the last two digits of a number must be divisible by 4 for the number to be divisible by 4. 37) i15566542489373798616517030354575401541545452

ALGEBRA II HONORS/GIFTED - SECTION 4-8 (Complex Numbers) Solve in your groups. x2 + 2x – 24 = 0 6x2 + 19x + 10 = 0 x2 – 8x + 25 = 0 x2 – 4x – 1 = 0

Now humor me and do the following… ALGEBRA II HONORS/GIFTED - SECTION 4-8 (Complex Numbers) Take your answers, add them together and then take the opposite of your answer. Take your answers and multiply them together. Do you notice anything special????

ALGEBRA II HONORS/GIFTED - SECTION 4-8 (Complex Numbers) So……….. Standard Form : ax2 + bx + c = 0 if s1 and s2 are the solutions of a quadratic equation, then

Find the quadratic equation with the following solutions ALGEBRA II HONORS/GIFTED - SECTION 4-8 (Complex Numbers) Find the quadratic equation with the following solutions 38) 8 and -11

Like….a really important theorem…… Irrational and imaginary zeros for quadratic equations (really, any equations) must come in conjugate pairs.

ALGEBRA II HONORS/GIFTED - SECTION 4-8 (Complex Numbers) Find the quadratic equation with real-number coefficients if one or more solutions is (are) …

ALGEBRA II HONORS/GIFTED - SECTION 4-8 (Complex Numbers) Factor. My math teacher told me you can’t factor these. 43) x2 + 25 44) 64x2 + 49 45) 4x2 + 9 46) -9x2 - 25