Marvin Mccormick
2020-11-01
Answered

Find the principal argument and exponential form of $z=\frac{i}{1+i}$
If z=x+iy is a complex number

You can still ask an expert for help

SkladanH

Answered 2020-11-02
Author has **80** answers

Rewrite the above complex number in the usual form z=x+iy as follows.

Compare the complex number

The argument of a complex number z=x+iy is given by

Here, for

Since both

Hence, its principal argument is the same as

The exponential form of a complex number z=x+iy with principal argument theta is given by

For

Hence, the exponential form of

Thus, the principal argument of

asked 2020-11-08

Classify each of the following matrices according as it is (a) real, (b)
symmetric, (c) skew-symmetric, (d) Hermitian, or (e) skew-hermitian,
and identify its principal and secondary diagonals.

$\left[\begin{array}{ccc}1& 0& -i\\ 0& -2& 4-i\\ i& 4+i& 3\end{array}\right]$

$\left[\begin{array}{ccc}7& 0& 4\\ 0& -2& 10\\ 4& 10& 5\end{array}\right]$

asked 2022-06-26

Solve for $\alpha $ where ${0}^{\circ}\le \alpha \le {360}^{\circ}$, in $1+\sqrt{3}\mathrm{tan}\alpha -\mathrm{sec}\alpha =0$

asked 2022-06-22

Is the answer correct?

I had to simplify it:

${\mathrm{cos}}^{2}(\pi +x)+{\mathrm{cos}}^{2}(\frac{\pi}{2}+x)=-{\mathrm{cos}}^{2}(x)-{\mathrm{sin}}^{2}(x)=-({\mathrm{cos}}^{2}(x)+{\mathrm{sin}}^{2}(x))=-1.$

I had to simplify it:

${\mathrm{cos}}^{2}(\pi +x)+{\mathrm{cos}}^{2}(\frac{\pi}{2}+x)=-{\mathrm{cos}}^{2}(x)-{\mathrm{sin}}^{2}(x)=-({\mathrm{cos}}^{2}(x)+{\mathrm{sin}}^{2}(x))=-1.$

asked 2022-07-09

If $\frac{\mathrm{sin}(x)}{a}=\frac{\mathrm{cos}(x)}{b}$ then $a\mathrm{sin}(2x)+b\mathrm{cos}(2x)=?$

$b\mathrm{sin}(x)=a\mathrm{cos}(x)$

$\mathrm{tan}(x)=\frac{a}{b}$

I couldn't simplify after that.

$b\mathrm{sin}(x)=a\mathrm{cos}(x)$

$\mathrm{tan}(x)=\frac{a}{b}$

I couldn't simplify after that.

asked 2022-02-25

I want to prove that

$2\mathrm{arctan}\sqrt{x}=\mathrm{arcsin}\frac{x-1}{x+1}+\frac{\pi}{2}$

asked 2022-06-12

Write as a single trigonometric function: $\frac{2\mathrm{tan}4\theta}{5-5{\mathrm{tan}}^{2}4\theta}$

asked 2022-04-21

How to compute the following trigonometric question

$\sqrt{2}\mathrm{sin}10(\mathrm{sec}5+\frac{2\mathrm{cos}40}{\mathrm{sin}5}-4\mathrm{sin}35)$