2What is a Complex Number??? A complex number is made up of two parts – a real number and an imaginary number.Imaginary numbers are defined to be the square root of -1a biReal Part Imaginary Part
3COMPLEX NUMBERSMain RulesWhere i is imaginaryExamples1)2)
4The Complex Number Plane 2iBecause a complex number is made up of a real and an imaginary value, the complex number plane is different than an xy coordinate plane.i-2-112-iSay we want to know where 2 – 2i would be-2iWe would go left or right for the real part and up or down for the imaginary part.
5Finding Absolute Value Ex: |3 - 4i|The Absolute Value of a complex number is the distance away from the origin on the complex number plane.You can find the absolute value by using the Pythagorean Theorem. In general,5|a + bi|=
6Additive Inverses of Complex Numbers Remember that to get the additive inverse of something, you simply multiply everything by a negativeEx: The additive Inverse of -5 is 5Therefore, what is the additive inverse of 5 – 2i?-5 + 2i
7Complex Number Operations Combining like terms (adding or subtracting)(5 + 7i) + (-2 + 6i)(Hint: treat the imaginary i like a variable)3 + 13iMultiplying Complex Numbers(12i)(7i)84 i2 =84 (-1) =-84
8You can even FOIL Complex Numbers! (6 – 5i)(4 – 3i) =24 – 20i -18i + 15i224 – 38i + 15(-1)24 – 15 – 38i9 – 38iNow, try a couple on your own:A) (2 + 3i)(-3 + 5i)B) (4 – 9i)(4 + 3i)-21 + i43 – 24i