Question

I^50

Answer this question, include your reasoning and steps.

Answer 1

(i)⁵⁰ = -1

Explanation:

The problem is,

→ (i)⁵⁰

Formula we use,

→ i² = -1

Let's solve the problem,

→ (i)⁵⁰

→ (i²)²⁵

→ (-1)²⁵

→ -1

Hence, the answer is -1.

Answer 2

-1

Explanation:

Given:

`i^(50)`

Rewrite 50 as the product of 2 and 25:

`\implies i^((2 \cdot 25))`

`\textsf{Apply the exponent rule} \quad a^(bc)=(a^b)^c:`

`\implies \left(i^2\right)^(25)`

Apply the imaginary number rule i² = -1 :

`\implies \left(-1\right)^(25)`

`\textsf{Apply the exponent rule} \quad (-a)^n=-a^n,\:\: \textsf{ if }n \textsf{ is odd}:`

`\implies -1^(25)`

As 1²⁵ = 1 then:

`\implies -1`