For a complex number z =x + iy, the argument theta satisfies - answer-tantheta = y/x
For a complex number z with |z| = r and arg(z) = theta, the modulus-argument form of z is - answer-z = r(cos(theta) + isin(theta))
For any complex number z = a + bi, the complex conjugate of the number is def...
Edexcel Further Maths Core Pure Year 1
(nΣr=1) (f(r) + g(r)) = - answer-(nΣr=1) f(r) + (nΣr=1) g(r)
(nΣr=1) kf(r) = - answer-k(nΣr=1) f(r)
Argand diagram - answer-- Represents complex numbers
- x-axis is the real axis and y-axis is the imaginary axis
- z = x + iy is represented by the point P(x,y) where x and y are Cartesian coordinates
Argument of a complex number - answer-the angle its corresponding vector makes with the
positive real axis
Complex number - answer-Written in the form a + bi, where a, b ∈ R
Complex numbers can be added or subtracted by - answer-adding or subtracting their real parts
and adding or subtracting their imaginary parts
For a complex number z = x + iy, the modulus is given by - answer-|z| = root(x² + y²)
For a complex number z =x + iy, the argument theta satisfies - answer-tantheta = y/x
For a complex number z with |z| = r and arg(z) = theta, the modulus-argument form of z is -
answer-z = r(cos(theta) + isin(theta))
For any complex number z = a + bi, the complex conjugate of the number is defined as -
answer-z* = a - bi
For any two complex numbers z1 and z1, arg(z1z2) = - answer-arg(z1) + arg(z2)
For any two complex numbers z1 and z2, |z1/z2| = - answer-|z1|/|z2|
For any two complex numbers z1 and z2, arg(z1/z2) = - answer-arg(z1) - arg(z2)
For any two complex numbers z1 and z2' |z1z2| = - answer-|z1||z2|
For two complex numbers z1 = x1 + iy1 and z2 = x2 + iy2, |z2 - z1| represents - answer-the
distance between the points z1 and z2 on an Argand diagram
Given z1 = x1 + iy1, and z2 = x2 + iy2, the locus of points z on an Argand diagram such that |z -
z1| = |z - z2| is - answer-the perpendicular bisector of the line segment joining z1 and z2
Given z1 = x1 + iy1, the locus of point z on an Argand diagram such that |z - z1| = r, or |z - (x1 +
iy1)|, is - answer-a circle with centre (x1,y1) and radius r.
Given z1 = x1 + iy1, the locus of points z on an Argand diagram such that arg(z - z1) = theta is -
answer-a half line from, but not including, the fixed point z1, making an angle theta with a line
from the fixed point z1 parallel to the real axis
half line - answer-A straight line extending from a point infinitely in one direction only
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through EFT, credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying this summary from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller TOPDOCTOR. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy this summary for R117,63. You're not tied to anything after your purchase.
