FP1 Flashcards
what are the steps for proof by induction?
prove it works for n=1assume it works for n=kprove it works for n=k+1
what is the complex conjugate of z?
Z with the sign of the imaginary part reversed.
If given a fraction with a complex denominator, how can it be written in the form a+bi?
Act as if you were rationalising the denominator. Multiply the bottom by a-bi and it should remove imaginary parts from the bottom.
what does z* mean?
the complex conjugate of z
find a and b such that (15+8i)^0.5=a+bi
square both sides.15+8i=(a+bi)(a+bi)expand the right side to get 15+8i=a²-b²+2abithus 8=2ab and 15=a²-b². Solve simultaneously.
what does [z] mean on an argand diagram?
the distance from the point z, to the origin.
how would the area 3 ≥[z] be represented?
A shaded in circle of radius 3 centre of (0,0)
how would you represent [z-(6+8i)]=10 ?
a circle of centre 6,8 and radius 10.
how would you represent [z=2+4i]=0
a point at -2,4
how would you represent Re(z)=-2
A infinite vertical line going through -2 on the x axis.
how would you represent [z]=[z-4]?
a vertical line going though 2 on the x axis.
how would you represent [z]≥[z-2i]
a horizontal line goes through 2 on the y axis and everything above it is shaded.
what is arg(z)?
the angle between the line real axis and the line of z.
how would you draw ? arg(z-6)=pi/4
A line goes from 6 =0i and makes an angle of pi/4 with the real axis.
write -12 + 5i in modulus argument form.
first find the modulus. In this case, it is 13.then find the angle between the line going from the origin to the point -12, 5. It is 2.75z=13(cos(2.75)+isin(2.75))
