1 - Complex Numbers Flashcards
What is √-1?
Imaginary number, i.
What is an imaginary number?
A number in the form bi, where b is real.
What is a complex number?
A number in the form a + bi where a and b are real.
How do you add/subtract complex numbers?
Add/subtract the real parts and imaginary parts separately.
How do you multiply a real number by a complex number?
Multiply out breackets.
What happens if b^2-4ac <0?
There are two distinct complex roots.
What is i^2?
-1.
What is the complex conjugate of z = a +bi.
z* = a - bi.
How do you divide two complex numbers?
Like rationalising the denominator.
What is true if two roots of a quadratic equation are non-real complex numbers?
They occur as a conjugate pair.
If the roots are a and b, how can you write the equation?
.(z-a)(z-b) = 0.
.z^2 - (a+b)z + ab = 0.
if a polynomial with real coefficients has root z, what is another root?
z*.
What are the possibilities of roots in a cubic equation?
.All real.
.One real and others form a complex conjugate pair.
What are the possibilities of roots in a quartic equation?
.All real.
.Two real, two complex conjugate pair.
.Two complex conjugate pairs.
