 Recent questions in Precalculus kihanja20 2022-01-18 Answered

What is the sum of this imaginary number series problem: $$\displaystyle{i}+{2}{i}^{{{2}}}+{3}{i}^{{{3}}}+{4}{i}^{{{4}}}+{5}{i}^{{{5}}}+\ldots+{2002}{i}^{{{2002}}}$$? Jean Blumer 2022-01-18 Answered

How do you simplify $$\displaystyle-{9}-{9}{i}\div-{1}-{8}{i}$$? Brock Brown 2022-01-18 Answered

How do you divide $$\displaystyle{\frac{{-{2}-{5}{i}}}{{{3}{i}}}}$$? sputneyoh 2022-01-18 Answered

How do you simplify $$\displaystyle{\frac{{{7}{i}}}{{{8}+{i}}}}$$? Joan Thompson 2022-01-18 Answered

How do I find the complex conjugate of $$\displaystyle{\frac{{{12}}}{{{5}{i}}}}$$? Danelle Albright 2022-01-18 Answered

How do you simplify $$\displaystyle{\left(-{i}\right)}^{{{3}}}$$? 2022-01-17

Problem finding zeros of complex polynomial $$\displaystyle{z}^{{{2}}}+{\left(\sqrt{{{3}}}+{i}\right)}{\left|{z}\right|}\overline{{{z}}}^{{{2}}}={0}$$ 2022-01-17

What's the thing with $$\displaystyle\sqrt{{-{1}}}={i}$$ 2022-01-17

Determine the set of values of $$\displaystyle{\exp{{\left({\frac{{{1}}}{{{z}}}}\right)}}}$$ for $$\displaystyle{0}{ < }{\left|{z}\right|}{ < }{r}$$ 2022-01-17

Why is $$\displaystyle\sqrt{{-{x}^{{{2}}}}}={\left|{x}\right|}{i}$$ So, $$\displaystyle{i}=\sqrt{{-{1}}}$$ 2022-01-17

Is there a problem in defining a complex number by $$\displaystyle{z}={x}+{i}{y}?$$ 2022-01-17

What are the rules for complex-component vectors and why? 2022-01-17

How to solve that quadratic complex equation? $$\displaystyle{\frac{{{z}^{{{2}}}-{1}}}{{{z}^{{{2}}}+{z}+{1}}}}$$ So, there can't be any z that makes null the denominator, $$\displaystyle{z}^{{{2}}}+{z}+{1}={0}$$ and after decomposing z, $$\displaystyle{x}^{{{2}}}-{y}^{{{2}}}+{x}+{2}{x}{y}{i}+{y}{i}={0}$$ 2022-01-17

Find $$\displaystyle{\left|{w}\right|}$$ without finding w? w is a complex number that satisfy: $$\displaystyle{5}{w}^{{{3}}}-{3}{i}{\left|{w}\right|}^{{{2}}}-{2}{i}={0}$$ Can we find $$\displaystyle{\left|{w}\right|}$$ without finding w or easy root? 2022-01-17

How to prove Euler's formula: $$\displaystyle{e}^{{{i}\phi}}={\cos{{\left(\phi\right)}}}+{i}{\sin{{\left(\phi\right)}}}?$$ 2022-01-17

Adding powers of i I've been struggling with figuring out how to add powers of i. For example, the result of $$\displaystyle{i}^{{{3}}}+{i}^{{{4}}}+{i}^{{{5}}}$$ is 1. But how do I get the result of $$\displaystyle{i}^{{{3}}}+{i}^{{{4}}}+\cdots+{i}^{{{50}}}$$? Writing it all down would be pretty mundane. 2022-01-17

How can you find the complex roots of i? A variation of the Root of Unity problem. I want to find all possible answers to this: $$\displaystyle{z}^{{{n}}}={i}$$ Where $$\displaystyle{i}^{{{2}}}=-{1}$$ 2022-01-17

Solve $$\displaystyle{z}^{{{2}}}-{6}{z}+{25}$$ into complex conjugate 2022-01-17

Argument of the summ of two complex numbers Let r, s be positive real numbers and $$\displaystyle\theta,\ \phi$$ real numbers with $$\displaystyle{\left|\theta-\phi\right|}{ < }\pi$$. Then an argument of $$\displaystyle{r}{e}^{{{i}\theta}}+{s}{e}^{{{i}\phi}}$$ lies between $$\displaystyle\theta$$ and $$\displaystyle\phi$$ Can someone give a short, clean proof of the statement above that doesn't rely on geometric intuition? 2022-01-17

Complex-number inequality $$\displaystyle{\left|{z}_{{{1}}}{z}_{{{2}}}\cdots{z}_{{{m}}}-{1}\right|}\leq{e}^{{{z}_{{{1}}}-{1}{\left|+\cdots+\right|}{z}_{{{m}}}-{1}{\mid}}}-{1}$$ Can anybody tell me how to prove the following inequality?

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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