Precalculus Solutions | Expert Assistance for Problems & Examples

How do you simplify $5 i \cdot i$ ?

Mary Keefe 2022-01-15

Multiply and simplify the following complex numbers:
$(- 3 - 2 i) \times (- 4 + 2 i)$

Joyce Smith 2022-01-15

Multiply each complex number by its complex conjugate.
a) $3 + 6 i$
b) $2 - 5 i$

Donald Johnson 2022-01-15

Factor the expressions over the set of complex numbers. For assistance, consider these examples
In Section R.3 we saw that some expressions factor over the set of integers. For example: $x^{2} - 4 = (x + 2) (x - 2)$
Some expressions factor over the set of irrational numbers. For example: $x^{2} - 5 = (x + \sqrt{5}) (x - \sqrt{5})$
To factor an expression such as $x^{2} + 4$ , we need to factor over the set of complex numbers. For example, verify that $x^{2} + 4 = (x + 2 i) (x - 2 i)$
a) $x^{2} - 9, x^{2} + 9$
b) $x^{2} - 100, x^{2} + 100$
c) $x^{2} - 64, x^{2} + 64$

reproacht3 2022-01-15

Plot the complex numbers 5i and $- 8 + 7 i$ in the complex plane.

Joanna Benson 2022-01-15

How do I solve $a r g (\frac{z - i}{z + i}) = \frac{π}{4}$ ?

garnentas3m 2022-01-15

What is $0^{i}$ ?

Carol Valentine 2022-01-15

How do you divide $\frac{3 + 9 i}{- 6 - 6 i}$ ?

Carla Murphy 2022-01-15

How do you write the complex conjugate of the complex number $\sqrt{- 15}$ ?

diferira7c 2022-01-15

Write the complex number $\frac{- 5 - 3 i}{4 i}$ in standard form?

Annette Sabin 2022-01-15

Solve $2 \cos^{2} x + \sin x = 1$ for all possible x

Kathy Williams 2022-01-15

Solving $\tan 2 x = 1 + 2 \sin 4 x$

lunnatican4 2022-01-15

What is the period of the $f (x) = \sin x + \sin 3 x$ ?
$f (x) = \sin x + \sin 3 x = 2 \frac{3 x + x}{2} \cos \frac{x - 3 x}{2} = 2 \sin 2 x \cos x = 4 \sin x \cos^{2} x$
$f (x + T) = 4 \sin (x + T) \cos^{2} (x + T) = 4 \sin x \cos^{2} x$

Juan Hewlett 2022-01-15

What is $\arctan (z_{1}) \pm \arctan (z_{2})$ with $z_{1}, z_{2} \in C$
On wikipedia, there is the following identity:
$\arctan (u) \pm \arctan (v) = \arctan (\frac{u \pm v}{1 \mp u v})$
However when I try some $u, v \in C$ to check, the formula does not hold. Is there an equivalent formula for complex numbers?

Teddy Dillard 2022-01-14

How can I rewrite $\sin^{3} (x) + \csc^{3} (x)$ ?
If $m = \sin x + \csc x$ compute:
$R = \sin^{3} x + \csc^{3} x$
how can I rewrite this expression

prsategazd 2022-01-14

Evaluate
$\cos θ \cos 2 θ \cos 3 θ + \cos 2 θ \cos 3 θ \cos 4 θ + \dots$
upto n terms

guringpw 2022-01-14

If $\sin α + \cos α = - \frac{\sqrt{7}}{2}$ , then $α$ is the angle of which quadrant?
My attempts:
$\sqrt{2} \sin (\frac{π}{4} + α) = - \frac{\sqrt{7}}{2}$
$\sin (\frac{π}{4} + α) = - \frac{\sqrt{14}}{4}$

Chris Cruz 2022-01-14

Can I put $x = \frac{π}{2}$ in $\tan 2 x = \frac{2 \tan x}{1 - \tan^{2} x}$ ?

Irrerbthist6n 2022-01-14

How would I go about finding the roots of $(e^{x} - 1) - k \arctan (x) = 0$ ?

Susan Nall 2022-01-14

For $α \in (0^{\circ}; 90^{\circ})$ simplify $\sin^{2} α + \tan^{2} α + \sin^{2} α \cdot \cos^{2} α + \cos^{4} α$
My try: $\sin^{2} α + \tan^{2} α + \sin^{2} α \cdot \cos^{2} α + \cos^{4} α = \sin^{2} α + \frac{\sin^{2} α}{\cos^{2} α} + \sin^{2} α \cdot \cos^{2} α + \cos^{4} α$
$= \frac{\sin^{2} α \cdot \cos^{2} α + \sin^{2} + \sin^{2} α \cdot \cos^{4} α + \cos^{6} α}{\cos^{2} α}$

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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