Question

Evaluate this i37*1/i67

Answer 1

Answer:

$i^{37}\times \frac{1}{i^{67}}=-1$

Step-by-step explanation:

Given : Expression $i^{37}\times \frac{1}{i^{67}}$

To find : Evaluate the expression ?

Solution :

We can write,

$i^{37}\times \frac{1}{i^{67}}=i^{36}\cdot i\times \frac{1}{i^{66}\cdot i}$    

We know that, $i=\sqrt{-1}\Rightarrow i^2=-1$

So, $i^{36}=i^{2\cdot 18}=(-1)^{18}=1$

$i^{66}=i^{2\cdot 33}=(-1)^{33}=-1$  

Substitute back,

$=i\times \frac{1}{-i}$

$=-1$

Therefore, $i^{37}\times \frac{1}{i^{67}}=-1$