complex numbers

Question 1

i = ?
i² = ?

Answer 1

i = √-1
i² = -1

Question 2

what is an imaginary number

Answer 2

bi
where b = any real number

Question 3

complex number

Answer 3

a + bi
a,b are any real numbers

Question 4

what does it mean if b² - 4ac < 0

Answer 4

ax² + bx + c = 0 has two distinct complex roots (neither are real)

Question 5

complex conjugate

Answer 5

if z = a + bi
z* = a - bi

Question 6

how to write a quadratic equation using its roots μ and §

Answer 6

(z - μ)(z - §) = 0
z² - (μ + §)z + μ§ = 0

Question 7

what to do if given one root of f(z)

Answer 7

if z¹ is a root of f(z)
z*¹ is also a root of f(z)

Question 8

roots for a cubic equation with real coefficients

Answer 8

Either:
• all three roots are real
or
• one root is real and the other two roots form a complex conjugate pair

Question 9

roots for a quartic equation with real roots

Answer 9

either:
• all four roots are real
or
• two toots are real and other two form a complex conjugate pair
or
• two pairs of four roots form two complex conjugate pairs