Question

The argument of 1/i is equal to

Answer 1

Answer:

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Answer 2

Answer:

The argument of the number $\frac{1}{i}$ = 90°

Step-by-step explanation:

To find,

The argument of the number $\frac{1}{i}$

Solution:

Recall the formula

Let z = a+ib,

Then the argument of the complex number z is given by

arg(z) = $tan^{-1}(\frac{b}{a})$

The given number is  $\frac{1}{i}$

The conjugate of this number is 'i'

 $\frac{1}{i}$×$\frac{i}{i}$ = $\frac{i}{i^2}$

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

= -i

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

Comparing with a+ib we get,

a = 0 and b = -1

The argument of  $\frac{1}{i}$ =  $tan^{-1}(\frac{b}{a})$

=  $tan^{-1}(\frac{-1}{0})$

= tan⁻¹(∞)

= 90°

The argument of the number $\frac{1}{i}$ = 90°

#SPJ3