Question

express the complex number in polar form
z=3+i√5​

Answer 1

Step-by-step explanation:

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Question

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Convert the given complex number in polar form :

3

+i

Medium

Solution

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Given complex number is

3

+i

Let rcosθ=

3

and rsinθ=1

On squaring and adding, we obtain

r

2

cos

2

θ+r

2

sin

2

θ=(

3

)

2

+1

2

⇒r

2

(cos

2

θ+sin

2

θ)=3+1

⇒r

2

=4

⇒r=

4

=2 [ Conventionally, r>0]

∴2cosθ=

3

and 2sinθ=1

⇒cosθ=

2

3

and sinθ=

2

1

∴θ=

6

π

[ As θ lies in the I quadrant ]

∴

3

+i=rcosθ+irsinθ=2cos

6

π

+i2sin

6

π

=2(cos

6

π

+isin

6

π

)

This is the required polar form.