IMAGINARY NUMBERS AND DEMOIVRE’S THEOREM Dual 8.3

Remember Complex Numbers: a + b i a = real number b = imaginary number Plot the following points i 2 – i 4i -3

Converting Rectangular to Polar Form Polar form of a Complex number: Rem: if x neg add 180 If y only neg. add 360 a (or x) b (or y) a+bi x = r cos (θ) y = r sin (θ) a + b i

Example:

Converting Polar to Rectangular Form x = r cos (θ) y = r sin (θ) Example:

Operations with Complex Numbers: All these can be worked much easier in POLAR FORM.

MULTIPLICATION Multiplying in Polar form

DIVISION

POWERS AND ROOTS Formula:

INDIVIDUAL ROOT

ALL ROOTS 3 solutions  1 real and 2 imaginary Change to complex Add 360 Conjugate pairs