Complete Textbook p. 4 - #s1-6 p. 5 - #s 1-6 WARM-UP: Simplifying Radicals Complete Textbook p. 4 - #s1-6 p. 5 - #s 1-6

in a math class far, far away.. A long long time ago, in a math class far, far away.. There was no way to take the square root of a negative number

Every time we squared a negative number We got a positive.

(-1) = 1 (-2) = 4 (-3) = 9

that when multiplied by itself Was there a number, that when multiplied by itself Gave you a negative???

Can we in fact, take the square root of a negative number? WE CAN!!!!

Ladies and Gentlemen of Algebra II I present to you a NEW number... A number so complex...

It stretches the imagination.. I present to you:

You can't take the square root of a negative number, right? When we were young and still in Coordinate Algebra, no numbers that, when multiplied by themselves, gave us a negative answer.  Squaring a negative number always gives you a positive.   (-1)² = 1. (-2)² = 4 (-3)² = 9

So here’s what the math people did: They used the letter “i” to represent the square root of (-1). “i” stands for “imaginary” So, does really exist?

Examples of how we use

Examples of how we use

Complex Numbers Objective: You will write, add, subtract, multiply, and divide complex numbers.

a + bi: the standard form of complex numbers - where a and b are real numbers a = the real part of the complex number bi = the imaginary part of the complex number b = the coefficient of the imaginary number

Every real number is a complex number because a = a + 0i . Complex Numbers Real Numbers Imaginary Numbers Every real number is a complex number because a = a + 0i . Every imaginary number is a complex number because bi = 0 + bi .

Imaginary Numbers i = i1 = i i5 = i2 = -1 i6 = i3 = i7 = i4 = i8 =