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Polar form of i to the power25 whole to the power 3

Amar kumar , 7 Years ago
Grade 11
anser 1 Answers
Omprakash Narenda

Last Activity: 7 Years ago

Whenever the power  of i is a multiple of 4, its value is 1.
(i25)3 = (i24 x i)3
= i3 
= i2 x i = – i 
Now,
- i can also be written in the cartesian form as 0 – i
Now 0 -i can also we be written in the polar form as r(cos\Theta + isin\Theta)
\therefore 0 – i = r(cos\Theta + isin\Theta)
Now,
Taking the modulus of 0 – i which is also equal to r in the graph,
Modulus(Here) = 1
\therefore r = 1
\therefore 0 – i = cos\Theta +isin\Theta
Comparing on both sides,
0 = cos\Theta 
-1 = sin\Theta
Therefore \Theta lies in 4th quadrant
\Rightarrow \Theta = \Pi./2
\therefore Polar form of  0-i = cos \Pi/2 +isin\Pi /2
 

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