Question

1, i, j

Answer 1

\[
\rho e^{i\theta + j\phi }
\]

Answer 2

\[a= \cos \theta \cos \phi \\ b = \sin \theta \cos \phi \\ c = \sin \phi\]

Answer 3

\[\sqrt{a^2+b^2+c^2}=1\]

Answer 4

\[
a(1)+b(i)+c(j)
\]

Answer 5

\[
f(\theta)f(\theta') =f(\theta+\theta')
\]

Answer 6

\[
\exp(x)
\]

Answer 7

\[
\exp_2(x,y)
\]

Answer 8

\[\LARGE e^{i \theta + j \phi} = f(\theta, \phi) + i g(\theta, \phi) + j h(\theta, \phi)+ijk(\theta, \phi)\]

Answer 9

\[e^{i a+b}=\cos (a+b)+i \sin(a+b) \\ e^{ia}e^{ib}=(\cos (a)+i \sin(a) )(\cos (b)+i \sin(b) )\]

Answer 10

\[\Huge
e_2^{(i\theta,j\phi)}
\]

Answer 11

\[
f(e^{i\theta}\times e^{j\phi})
\]

Answer 12

\[
\exp(i\theta) = \cos(\theta)+i\sin(\theta)
\]

Answer 13

\[
\exp_2(i\theta,j\phi) = \cos(\theta)\cos(\phi) +i\sin(\theta)\cos(\phi) +j\sin(\phi)
\]

Answer 14

\[\Large e^{i \theta + j \phi}=e^{i(\theta - ij \phi)}=\cos(\theta-ij \phi)+i \sin(\theta-ij \phi)\]

Answer 15

\[e^x=\cosh x+\sinh x \\ =e^{i(-ix)}=\cos(-ix)+i \sin(-ix) \\ = \cos(ix)-i \sin(ix)\] \[\cosh(x) = \cos(ix)\]\[\sinh (x) = -i \sin(ix)\]

Answer 16

\[\large e^{j \frac{\phi}{2}}\]

Answer 17

\[\LARGE j = e^{j \frac{\pi}{2}}\]

Answer 18

\[
i = e^{i\pi/2} =
\]

Answer 19

\[
f(i,j) = f(j,i)
\]

Answer 20

\[
e^{i\theta +a}
\]

Answer 21

\(\color{blue}{\text{Originally Posted by}}\) @wio
\[
e^{i\theta +a}=e^ae^{i\theta}
\]
\(\color{blue}{\text{End of Quote}}\)

Answer 22

\[
\cos(i\theta+a)+i\sin(i\theta+a)
\]

Answer 23

\[(\cos \theta + i \sin \theta)(\cosh a + \sinh a)\]