Complex numbers

Question 1

What is a complex number

Answer 1

a number with a real (Re) and imaginary (Im) part
written as a + bi

Question 2

what is i

Answer 2

square root of -1

Question 3

square root of, for example -16

Answer 3

4i
same as normal but add i

Question 4

Order of number sets

Answer 4

natural - integer - rational - real - complex

Question 5

how to equate 2+ complex numbers

Answer 5

put real numbers together and complex together then equate separately

Question 6

multiplying and dividing complex numbers

Answer 6

same as real - multiply out brackets then simplify
or rationalise denominator

Question 7

how can you tell when quadratics have complex roots

Answer 7

b^2 - 4ac will be less than 0
you can solve in the normal way by using i at the negative square root

Question 8

how to make an equation with complex roots

Answer 8

write down (z - root 1)(z - root 2) then expand
root 1 and root 2 will be complex conjugates

Question 9

How to draw argand diagrams

Answer 9

represent real part on x axis and imaginary part on y axis

Question 10

what is the addition/ subtraction of complex numbers on a diagram similar to

Answer 10

vectors - combine to show sum and use opposite direction vectors to subtract

Question 11

what should conjugates/ complex quadratic roots look like on an argand diagram

Answer 11

have the same x (real) value and reflect in the x (real axis)

Question 12

what should real numbers look like on an argand diagram

Answer 12

stay on the x (real axis)
because real numbers are complex as in a + bi a is just 0

Question 13

what condition needs to be fulfilled for complex roots to be conjugates

Answer 13

in ax2 + bx + c, a b and c must all be real numbers