Complex Numbers with In-Depth Explanation

If the equation ${(z + 1)}^{7} + z^{7} = 0$ has roots $z_{1}, z_{2}, \dots z_{7}$
then what is the value of $\sum_{r = 1}^{7} R (Z_{r}) ?$

2022-01-17

How can you determine all of the zeroes (real and imaginary) of the polynomial function:
$P (x) = x^{4} + 2 x^{3} - 9 x^{2} - 10 x - 24 ?$

2022-01-17

How do I solve this equation in complex numbers
$4 {\overset{―}{z}}^{2} - 4 z | z | + 3 = 0 ?$

2022-01-17

How can we prove that $| z | \leq R e (z) ?$

2022-01-17

Why is $e^{i θ} = \cos (θ) + i \sin (θ) ?$

2022-01-17

What is the analytic function $f (z)$ in terms of z whose real part is $e^{- x} (x \sin y - y \cos y)$ ?

2022-01-17

Do functions exist so that they map from Complexes to Reals?

2022-01-17

How can you show that
$\frac{1}{1 - \cos θ - i \sin θ} = \frac{1}{2} + \frac{i}{2} \times \cot \frac{θ}{2}$ where $i = \sqrt{- 1} ?$

2022-01-17

If I have given that the absolute value of Z is 1. how do I prove the $z + \frac{1}{z}$ is re and $z - \frac{1}{z}$ is Im?

2022-01-17

How do you factorize and find roots of the polynomial
${(1 + x)}^{n} - x^{n}$
(polynomials, complex numbers, roots, irreducible polynomials, weierstrass factorization, math)?

2022-01-17

Is $| \frac{a - i b}{a + i b} |$ equal to 1? If yes, how?

2022-01-17

How do you find the absolute value of the complex number $z = 3 - 4 i$ ?

2022-01-17

How do you simplify $2 \sqrt{- 49} + 3 \sqrt{- 64}$ ?

2022-01-17

How do you simplify $| 2 + 3 i | ?$

2022-01-17

How do you find the absolute value of $1 + 3 i$ ?

2022-01-17

How to express $e^{2 - i}$ in the form $a + i b$ ?

2022-01-17

How do you write the expression $i^{- 18}$ in the standart form $a + b i$ ?

Russell Gillen 2022-01-17

Why does $i^{2} = - 1 ?$

Carla Murphy 2022-01-17

How do I solve by de moivres theorem and in a final answer of polar form $({(c i s 2 θ)}^{- 3}) (\frac{{(c i s 5 θ)}^{2}}{{(c i s 3 θ)}^{4} ({(5 e^{j} 2 θ)}^{3}) ?}$

osnomu3 2022-01-17

How can you prove $e^{π i} + 1 = 0 ?$

Algebra is never easy even for those that claim to know it well. Regardless if you are solving quadratic equations with complex numbers or require someone to help you eliminate possible mistakes in your assignment, our list of equations will help you to find the most common answers.

The list of questions that you can see below serves as the basic examples of similar tasks. Solving complex tasks with the help of various examples also starts with probability, which is why remember to check your original problem twice to ensure that nothing is missed!

Algebra II

Complex numbers Explained: In-Depth Examples, Equations, and Expert Insights