1.4

i= -1 i 2 = -1

a+b i Real Imaginary part part

If b0 then a+bi is a complex number called an imaginary number If b=0 then a+bi is a real number If a=0 then bi is a pure imaginary number

-4 + 6i 2i = 0+2i 3=3+0i

Adding (a+bi)-(c+di)=(a+c)-(b+d)i (a+bi)+(c+di)=(a+c)+(b+d)i Subtracting (5-11i)+(7+4i) (5-2i)+(3+3i) (-5+i)-(-11-6i) (2+6i)-(12-i)

Use the distributive property and FOIL method After completing the multiplication replace i 2 with -1 4i(3-5i) (7-3i)(-2-5i)

For the complex conjugate a+bi, its complex conjugate is a-bi. The multiplication of complex conjugates results in a real number. (a+bi)(a-bi)=a 2 +b 2 (a-bi)(a+bi)=a 2 =b 2 The goal of the division procedure is to obtain a real number in the denominator. Example 7+4i 2-5i

The square root of 4i and-4i both result in -16. In the complex number system, - 16 has two square rolls, we use 4i as the principal square root.