Question

How is i⁵ = (i²)²

Complex numbers class 11
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Answer 1

Answer :

$\sf \mapsto \: \: {i}^{5} \not = ( {i}^{2} )^{2} = {i}^{4}$

Explanation :

Complex Number :

• square of complex numbers is -ve
• written as i (=√-1)

Hence,

$\mapsto \sf \: ( {i})^{5} = \: ( \sqrt{ - 1} ) {}^{5}$

$\mapsto \sf \boxed{ \sf{ i \times i \times i \times i }}\times i$

$\mapsto \sf \: {i}^{4} \times i$

$\mapsto \sf \: 1 \times i$

$\mapsto \sf \: \: i$

we usually use to express any imaginary Number as a+bi

for example 6+√-5 = 6+i√5

and polar form of a complex Number is r( cos x + i sin x )

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