A Level Further Maths Core Pure Exam Questions With Solved Solutions.
1 view 0 purchase
Course
A level Maths
Institution
A Level Maths
Form of complex numbers - Answer a + bi
Real and imaginary parts of z = a + bi - Answer Re(z) = a, Im(z) = b
When two complex numbers are equal, what is true - Answer Their real parts are equal and their imaginary parts are equal
i² - Answer -1
i³ - Answer -i
i⁴ - ...
A Level Further Maths Core Pure Exam
Questions With Solved Solutions.
Form of complex numbers - Answer a + bi
Real and imaginary parts of z = a + bi - Answer Re(z) = a, Im(z) = b
When two complex numbers are equal, what is true - Answer Their real parts are equal and their
imaginary parts are equal
i² - Answer -1
i³ - Answer -i
i⁴ - Answer 1
Determinant for two real roots (distinct roots) - Answer b² - 4ac > 0
Determinant for one real root (repeated roots) - Answer b² - 4ac = 0
Determinant for no real roots (two distinct complex roots) - Answer b² - 4ac < 0
Complex conjugate for z = a + bi - Answer z* = a - bi
Product zz* is always - Answer Real
Expansion of (z - α)(z - β) = 0 - Answer z² - (α + β)z + αβ = 0
, Possible Roots in a Cubic Equation - Answer Three real roots or one real root and a complex conjugate
pair of roots
Possible Roots in a Quartic Equation - Answer Four real roots or two real roots and a complex conjugate
pair of roots or two sets of conjugate pairs
x-axis on an argand diagram - Answer Real axis
y-axis on an argand diagram - Answer Imaginary axis
Modulus of a complex number |z| - Answer Distance from the origin to that number (on an Argand
diagram)
How do you calculate the modulus of a complex number |z|? - Answer √(x² + y²)
Argument of a complex number (arg z) - Answer Angle between the positive real axis and the line
joining that number to the origin (on an Argand diagram)
Modulus-argument Form - Answer z = r(cosθ + i sinθ)
| z₁ x z₂ | = - Answer | z₁ | | z₂ |
arg(z₁ x z₂) = - Answer arg z₁ + arg z₂
|(z₁/z₂)| = - Answer (| z₁ |)/(| z₂ |)
arg(z₁/z₂) = - Answer arg z₁ - arg z₂
Centre of Circle |z - (a + ib)| = r - Answer a, b
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 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 these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller TestSolver9. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $9.79. You're not tied to anything after your purchase.
