If z = r e^ i ,then | e^ iz |=

MCQ

If $z = r{e^{i\theta }},$then $|{e^{iz}}|$=

A
${e^{r\sin \theta }}$
✓
${e^{ - r\sin \theta }}$
C
${e^{ - r\cos \theta }}$
D
${e^{r\cos \theta }}$

✓

Answer

Correct option: B.

${e^{ - r\sin \theta }}$

b
(b)If $z = r{e^{i\theta }} = r(\cos \theta + i\sin \theta )$
==> $iz = ir(\cos \theta + i\sin \theta ) = - r\sin \theta + ir\cos \theta $
or ${e^{iz}} = {e^{( - r\sin \theta + ir\cos \theta )}} = {e^{ - \sin \theta }}{e^{ri\cos \theta }}$
or $|{e^{iz}}| = |{e^{ - r\sin \theta }}||{e^{ri\cos \theta }}|$$ = {e^{ - r\sin \theta }}|{e^{ir\,\cos \theta }}|$
$ = {e^{ - r\sin \theta }}{[\{ {\cos ^2}(r\cos \theta ) + {\sin ^2}(r\cos \theta )\} ]^{1/2}} = {e^{ - r\sin \theta }}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 11 - 4.1 complex nubers→STD 11 - 4.1 complex nubers — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Given that the term of the expansion $(x^{1/3} - x^{-1/2})^{15}$ which does not contain $x$ is $5\, m$ where $m \in N$, then $m =$

→

Slope of a line which cuts off intercepts of equal lengths on the axes is:

→

A chord $AB$ drawn from the point $A(0,3)$ on circle ${x^2} + 4x + {(y - 3)^2} = 0$ meets to $M$ in such a way that $AM = 2AB$, then the locus of point $M$ will be

→

If $f(x) = \left\{ {\begin{array}{*{20}{c}}{\frac{2}{{5 - x}},}&{{\rm{when \,\,}}x < 3}\\{5 - x,}&{{\rm{when\,\, }}x > 3}\end{array}} \right.$, then

→

For non-negative integers $n$, let

$f(n)=\frac{\sum_{k=0}^n \sin \left(\frac{k+1}{n+2} \pi\right) \sin \left(\frac{k+2}{n+2} \pi\right)}{\sum_{k=0}^n \sin ^2\left(\frac{k+1}{n+2} \pi\right)}$

Assuming $\cos ^{-1} x$ takes values in $[0, \pi]$, which of the following options is/are correct ?

$(1)$ $\sin \left(7 \cos ^{-1} f(5)\right)=0$

$(2)$ $f(4)=\frac{\sqrt{3}}{2}$

$(3)$ $\lim _{n \rightarrow \infty} f(n)=\frac{1}{2}$

$(4)$ If $\alpha=\tan \left(\cos ^{-1} f(6)\right)$, then $\alpha^2+2 \alpha-1=0$

→

If in an $A.P.,$ first term is $20,$ common difference is $2$ and nth term is $42,$ then find sum up to $n$ terms.

→

Number of principal solution of the equation $tan \,3x - tan \,2x - tan\, x = 0$, is

→

The acute angle between the medians drawn from the acute angles of a right angled isosceles triangle is:

→