Complex Numbers

Complex Numbers

• any number expressed in the form a + bi

• a and b are real numbers

• I is an imaginary number representing the square root of -1, where i² is -1

• Every complex number has a complex conjugate of a - bi

Converting Complex Numbers

• Complex numbers can be mapped in the form (a,b)

• To turn (a,b) into polar form, take the square root of a² + b² to get r²

• 0 = arctan (b/a)

• It can also be written in the form z = r(cos0 + isin0) or z = rcis(0)

• can be written in Euler’s form as z = re^i0

• demoivres theorem states that z^n = r^n(cosn0 + isin(n0)