Question

If z=√-5 then what is the imaginary part?
$z = \sqrt{ - 5}$
​

Answer 1

ANSWER IS 4.

EXPLANATION:)

z is a non-real complex number.

let z=re

iθ

(Imz)

5

Imz

5

=

r

5

sin

5

θ

r

5

sin5θ

say, f(θ)=

sin

5

θ

sin5θ

equating first derivative to 0

f

′

(θ)=0

⇒sin

5

θ⋅5cos5θ−sin5θ⋅5sin

4

θ⋅cosθ

⇒sinθ⋅cos5θ=cosθ⋅sin5θ

⇒tanθ=tan5θ

⇒θ=0,π/4...

but f(0) is indeterminate

f(π/4)=−4

∴ Minimum value of

(Imz)

5

Imz

5

is −4

Answer 2

ANSWER IS 4.

EXPLANATION:)

z is a non-real com

say, f(θ)=

sin

5

θ

sin5θ

equating first derivative to 0

f

′

(θ)=0

⇒sin

5

θ⋅5cos5θ−sin5θ⋅5sin

4

θ⋅cosθ

⇒sinθ⋅cos5θ=cosθ⋅sin5θ

⇒tanθ=tan5θ

⇒θ=0,π/4...

but f(0) is indeterminate

f(π/4)=−4

∴ Minimum value of

(Imz)

5

Imz

5

is −4