207 results for "complex".

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• Question

Find modulus and argument of two complex numbers.

Then use De Moivre's Theorem to find powers of the complex numbers.

• Exam (5 questions)

AEP Y1 - Engineering Mathematics Assessment 1(i)

Note that part(i) counts 20% towards the final Y1 Engineering Mathematics module grade.

• Exam (5 questions)

AEP Y1 - Engineering Mathematics Assessment 1(i)

Note that part(i) counts 20% towards the final Y1 Engineering Mathematics module grade.

• Exam (5 questions)

AEP Y1 - Engineering Mathematics Assessment 1(i)

Note that part(i) counts 20% towards the final Y1 Engineering Mathematics module grade.

• Question

Practice to decide which quadrant a complex number lies in.

• Question

Practice to decide which quadrant a complex number lies in.

• Exam (5 questions)

You are allowed 38 minutes to complete this test.

You may use rough paper for your calculations.

• Exam (5 questions)

You are allowed 31 minutes to complete this test.

You may use rough paper for your calculations.

• Question

Two parts.

• Exam (7 questions)

Content assessed : complex arithmetic; argument and modulus of complex numbers; de Moivre's theorem.

This complex numbers in-class assesment counts 20% towards your final maths grade for WM104.

Note that although questions are randomised for each student, all questions test the same learning outcomes at the same level for each student.

If you have any questions during the test, please put up your hand to alert the invigilator that you need attention.

• Question

Multiplication and addition of complex numbers. Four parts.

• Conditional visibility
Question in How-tos

Show one of several blocks of text depending on the value of a question variable.

As well as a simple check for the value of a variable, the condition to display a block of text can be a complex expression in any of the question variables - in this example, depending on the discriminant of the generated quadratic.

• Question

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $-\pi$ and $\pi$ and careful with quadrants!

• Question

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

• Question

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

• Question

Find the solution of a constant coefficient second order ordinary differential equation of the form $ay''+by=0$. Complex roots.

• Question

Find $\displaystyle I=\int \frac{2 a x + b} {a x ^ 2 + b x + c}\;dx$ by substitution or otherwise.

• Question

Polar form of a complex number.

• Question

Cauchy's integral theorem/formula for several functions $f(z)$ and $C$ the unit circle.

• Question

Modulus and argument of a single complex number, where $\mathrm{Re}(z)=\mathrm{Im}(z)$.

• Question

Modulus and argument of a single complex number $z=z_1/z_2$, where $\mathrm{Re}(z_1)=\mathrm{Im}(z_1)$ and $\mathrm{Re}(z_2)=-\mathrm{Im}(z_2)$.

• Question

Calculate the principal value of a complex number.

• Question

Write complex numbers in real-imaginary form.

• Question

Poles, residues, and contour integral of a complex-valued function.  Pair of pure imaginary poles.

• Question

Poles, residues, and contour integral of a complex-valued function.  Pair of real poles.

• Question

Poles, residues, and contour integral of a complex-valued function.  Single, simple pole.

• Question

Calculation of modulus, argument, multiplication by complex conjugate, given two complex numbers.

• Question

Contour integral of $z^2$ along any path.

• Question

Contour integral of $\mathrm{e}^{-z}$ along any path.

• Question

Contour integral of a complex-valued function $f(z)$ with the poles of $f(z)$ either inside or outside the path $C$.