7.7 Complex Numbers

Imaginary numbers and Powers of i

Square Roots of Negative #’s

Complex Numbers a is the real part Definition: Any number that can be written in the form a+bi a is the real part b is the coefficient of the imaginary part

Arithmetic Operations (3+7i) + (2-5i) = 5+2i • (3+7i) - (2-5i) = 1+12i • (3+7i)(2-5i) = 6-15i +14i -35i² = 6-i+35 =41-i

Complex Conjugates # conjugate 3+2i 3-2i 1-i 1+i 4i -4i 0+4i 0-4i 5 5 5 5 5+0i 5-0i

Dividing complex numbers • multiply numerator/denominator by conjugate of denominator • Ex.