Chapter 1 - Complex Numbers

what is i

√-1

what is an imaginary number

number in form bi

how is complex number written

a + bi

complex conjugate 

Z* a-bi

what does it mean if b² - 4ac< 0

quadratic equation ax² + bx + c has 2 distinct complex roots neither of which are real

i²

-1

i³

-i

i^4

1

if the roots of a quadratic equation are nonreal complex numbers what do they occur as

conjugate pairs

if the roots of a quadratic equation are α and β how canyou write equation

(z-α)(z-β) = 0

or z² - (α + β )z +αβ=0

in a cubic equation what must the roots be

• 3 rel roots

• one root is real and the other 2 roots form a complex conjugate pair

in a quartic equation what must the roots be 

• all four roots real

• 2 real roots and the other 2 form a complex conjugate pair

• 2 roots form a complex conjugate pair and the other 2 roots form a complex conjugate pair