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GradeEuler's Form, Euler's Form

TopicLatest Questions

If $z = 3 - 4i$ is turned ${90^0}$ in anti clock direction, then new position of $z$ is

A.$3 - 4i$

B.$4 - 3i$

C.$4 + 3i$

D.$3 + 4i$

A.$3 - 4i$

B.$4 - 3i$

C.$4 + 3i$

D.$3 + 4i$

Find the real part of \[z={{e}^{{{e}^{i\theta }}}}\], \[\theta \in R\].

If ${e^{i\theta }} = \cos \theta + i\sin \theta $ then in \[\Delta ABC\] value of ${e^{iA}}.{e^{iB}}.{e^{iC}}$ is

A) \[ - i\]

B) \[1\]

C) \[ - 1\]

D) None of these

A) \[ - i\]

B) \[1\]

C) \[ - 1\]

D) None of these

The amplitude of \[\sin \dfrac{\pi }{5} + i\left( {1 - \cos \dfrac{\pi }{5}} \right)\] is…

Verify the Euler’s formula for the given solid.

What does $\dfrac{{{e}^{ix}}-{{e}^{-ix}}}{2i}$ equal?

If $\Phi \left( N \right)$ is the number of integers which are less than $N$ and prime to it, and if $x$ is prime to $N,$ show that: ${{x}^{\Phi \left( N \right)}}-1\equiv 0\left( \bmod N \right).$

How do you evaluate \[{{e}^{\dfrac{\pi }{12}i}}-{{e}^{\dfrac{13\pi }{8}i}}\] using trigonometric functions?

How do you graphically divide complex numbers?

A root of \[{x^5} - 32 = 0\;\] lies in quadrant II. Write this root in polar form.

$2\left( {\cos {{120}^0} + i\sin {{120}^0}} \right)$

A. $2\left( {\cos {{144}^0} + i\sin {{144}^0}} \right)$

B. $2\left( {\cos {{150}^0} + i\sin {{150}^0}} \right)$

C. $4\left( {\cos {{144}^0} + i\sin {{144}^0}} \right)$

D. $2\left( {\cos {{72}^0} + i\sin {{72}^0}} \right)$

$2\left( {\cos {{120}^0} + i\sin {{120}^0}} \right)$

A. $2\left( {\cos {{144}^0} + i\sin {{144}^0}} \right)$

B. $2\left( {\cos {{150}^0} + i\sin {{150}^0}} \right)$

C. $4\left( {\cos {{144}^0} + i\sin {{144}^0}} \right)$

D. $2\left( {\cos {{72}^0} + i\sin {{72}^0}} \right)$

How does it relate \[e\] to \[\pi \] ?

How many edges are there in a cuboid?

(A) $3$

(B) $4$

(C) $5$

(D) $6$

(E) $12$

(A) $3$

(B) $4$

(C) $5$

(D) $6$

(E) $12$

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