Precalculus Solutions | Expert Assistance for Problems & Examples

What are the solutions for the equations $\cos Z = - i, 3 \sin Z + i \cos Z = e^{i z}, and e^{2 z} + 4 i = - 3 \sqrt{3} - 3 i$ ?

Chris Cruz 2022-01-17

Perform the indicated operation:
$7 [\cos (228^{\circ}) + i \sin (228^{\circ})] \times 8 [\cos (232^{\circ}) + i \sin (232^{\circ})]$

Shirley Thompson 2022-01-17

Multiply and simplify the following complex numbers:
$(- 3 + 3 i) \times (3 - 2 i)$

William Collins 2022-01-17

My work with complex numbers verified that the only possible cube root of 8 is 2. Determine whether the statement makes sense or does not make sense, and explain your reasoning.

kuhse4461a 2022-01-17

How do I solve $z^{2} = 2 + 2 r t 3 i$ ? For a quadratic I find $y^{2} - r t 2 y + 1 r t 3$ but my answer is nothing like a solve. Can someone advise?

elvishwitchxyp 2022-01-17

If $| Z 1 | = | Z 2 | and a r g z 1 \sim a r g z 2 = π$ , how do you show that $Z 1 + Z 2 = 0$ ?

Patricia Crane 2022-01-17

If $a + b + c = 0$ , and w is a complex root of cube roots of unity, then can you show that
${(a + b w + c w^{2})}^{3} + {(a + b w^{2} + c w)}^{3} = 27 a b c$ ?

Maria Huey 2022-01-17

How do I add the following? $Z 1 = 3 - \sqrt{- 2} and Z 2 = 4 + \sqrt{- 4}$ ?

John Stewart 2022-01-17

How do you show that the function $w = z e^{\overset{―}{z}}$ is nowhere analytic?

Reginald Metcalf 2022-01-17

Suppose $\frac{d}{d z} (f (z))$ exists at a point z. Is $\frac{d}{d z} (f (z))$ continuous at z?

expeditiupc 2022-01-17

How do you simplify $\sqrt{- 4} - \sqrt{- 25}$ ?

osteoblogda 2022-01-17

How do you simplify $\sqrt{- 2156}$ ?

aspifsGak5u 2022-01-17

How do you find the absolute value of $5 + 12 i$ ?

Painevg 2022-01-17

How do you simplify $i^{6} (2 i - i^{2} - 3 i^{3})$ ?

Kathleen Rausch 2022-01-17

How do you simplify $(- 10 i) (9 i) + 8$ ?

Reginald Metcalf 2022-01-17

How to solve sum of $\cos (k x)$ for the case $\cos (x) = 1$
I have the solution for $\sum_{{k = 1}}^{n} \cos (k x)$ :
$\sum_{k = 1}^{n} \cos (k x) = R (\sum_{k = 1}^{n} e^{i k x})$
$= R (e^{i x} \frac{e^{i n x} - 1}{e^{i x} - 1}) = R (\frac{e^{i x} e^{\frac{i n x}{2}}}{e^{\frac{i x}{2}}} \frac{e^{\frac{i n x}{2}} - e^{\frac{- i n x}{2}}}{e^{\frac{i x}{2}} - e^{\frac{- i x}{2}}}) = R (e^{\frac{i (n + 1) x}{2}} \frac{\sin \frac{n x}{2}}{\sin \frac{x}{2}}) = \frac{\sin \frac{n x}{2}}{\sin \frac{x}{2}} \cos (\frac{(n + 1) x}{2})$
but if $e^{i x} = 1$ i am dividing trough 0 in line 2. So i know that in this case $e^{i x} \neq 1$ . So my question is: What is the $\sum_{k = 1}^{n} \cos (k x) if e^{i x} = 1$

feminizmiki 2022-01-16

Evalute $\frac{\tan α - \cot α}{\sin^{4} α - \cos^{4} α}$ if $α$ is an acute angle and $\tan α = 2$

Mary Reyes 2022-01-16

Why is $\arctan (\tan (\frac{25 π}{4})) = \frac{π}{4}$ , and how can I get from the expression on the left to the one on the right?

Joseph Krupa 2022-01-16

I need some help answering this question:
$f (x) = \frac{cosh (x)}{sinh (x)} - \frac{1}{x}$
find the limit of f(x) as x tends to 0 by writing f(x) as a quotient of two powers series.
I have so far:
$\frac{(x (1 + \frac{x^{2}}{2!} + \frac{x^{4}}{4!} + \dots)) - (x + \frac{x^{3}}{3!} + \dots)}{x (x + \frac{x^{3}}{3!} + \dots)} = \frac{(x + \frac{x^{3}}{2!} + \frac{x^{5}}{4!} + \dots) - (x + \frac{x^{3}}{3!} + \dots)}{(x^{2} + \frac{x^{4}}{3!} + \dots)}$
but I don't know how to reduce this further.

veksetz 2022-01-16

Evaluate the following in terms of $α = lim_{x \to 0} \frac{\sin x}{x}$ :
$lim_{x \to 0} \frac{\tan^{2} (x) + 2 x}{x + x^{2}}$

Precalculus problems and solutions are hard to find online even though this topic is quite popular among college students majoring in Engineering. Keeping this fact in mind, we decided to provide you with a list of questions and answers that will help you with various precalculus problems. Regardless if it is related to equations or any other problem, these precalculus problems and composite functions examples and solutions below will help you see the logic and compare solutions as you check your original task.

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