2022-01-17

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

nick1337

Expert2022-01-18Added 777 answers

Step 1
Given: $|2+3i|$
$|a+bi|=\sqrt{{a}^{2}+{b}^{2}}$
So,
$|2+3i|=\sqrt{{2}^{2}+{3}^{2}}$
$\Rightarrow \sqrt{4+9}$
$\Rightarrow \sqrt{13}$
Hence, $|2+3i|=\sqrt{13}$

Vasquez

Expert2022-01-18Added 669 answers

Step 1
The inverse of $2+3i$ is $\frac{1}{2+3i}$
In general case, multiply the expression $\frac{1}{a+bi}$ by the conjugate (the conjugate of $a+ib$ is $a-ib$ ):
$\frac{1}{a+ib}=\frac{1}{(a-ib)(a+ib)}(a-ib)$
Expand the denominator: $\frac{1}{(a-ib)(a+ib)}(a-ib)=\frac{a-ib}{{a}^{2}+{b}^{2}}$
Split:
$\frac{a-ib}{{a}^{2}+{b}^{2}}=\frac{a}{{a}^{2}+{b}^{2}}-\frac{ib}{{a}^{2}+{b}^{2}}$
In our case, $a=2$ and $b=3$
Therefore, $(\frac{1}{2+3i})=(\frac{2}{13}-\frac{3i}{13})$
Hence, $\frac{1}{2+3i}=\frac{2}{13}-\frac{3i}{13}$

alenahelenash

Expert2022-01-24Added 556 answers

Step 1
We have that $a=2$ and $b=3$
Thus,
$r=\sqrt{(2{)}^{2}+(3{)}^{2}}=\sqrt{13}$
Also,
$\theta =a\mathrm{tan}(\frac{3}{2})=a\mathrm{tan}(\frac{3}{2})$
Therefore,
$2+3i=\sqrt{13}(\mathrm{cos}(a\mathrm{tan}(\frac{3}{2}))+i\mathrm{sin}(a\mathrm{tan}(\frac{3}{2})))$

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

Which operation could we perform in order to find the number of milliseconds in a year??

$60\cdot 60\cdot 24\cdot 7\cdot 365$ $1000\cdot 60\cdot 60\cdot 24\cdot 365$ $24\cdot 60\cdot 100\cdot 7\cdot 52$ $1000\cdot 60\cdot 24\cdot 7\cdot 52?$ Tell about the meaning of Sxx and Sxy in simple linear regression,, especially the meaning of those formulas

Is the number 7356 divisible by 12? Also find the remainder.

A) No

B) 0

C) Yes

D) 6What is a positive integer?

Determine the value of k if the remainder is 3 given $({x}^{3}+k{x}^{2}+x+5)\xf7(x+2)$

Is $41$ a prime number?

What is the square root of $98$?

Is the sum of two prime numbers is always even?

149600000000 is equal to

A)$1.496\times {10}^{11}$

B)$1.496\times {10}^{10}$

C)$1.496\times {10}^{12}$

D)$1.496\times {10}^{8}$Find the value of$\mathrm{log}1$ to the base $3$ ?

What is the square root of 3 divided by 2 .

write $\sqrt[5]{{\left(7x\right)}^{4}}$ as an equivalent expression using a fractional exponent.

simplify $\sqrt{125n}$

What is the square root of $\frac{144}{169}$