Grade 11Algebra

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

Amar kumar

9 Years agoGrade 11

1 Answer

Omprakash Narenda

9 Years ago

Whenever the power of i is a multiple of 4, its value is 1.

(i²⁵)³ = (i²⁴x i)³

⁼i³

⁼i²x 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 4^th quadrant

$\Rightarrow$ $\Theta$ = $\Pi$ ./2

$\therefore$ Polar form of 0-i = cos $\Pi/2 +isin\Pi /2$

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

Amar kumar

1 Answer

Omprakash Narenda

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