Question

write the polar form of root of -5 +12i​

Answer 1

Explanation:

To convert a complex number

x

+

i

y

into the polar form:

(i) We find

r

=

√

x

2

+

y

2

.

(ii) We find

α

=

tan

−

1

∣

∣

y

x

∣

∣

.

(iii) We find

θ

depending upon the quadrant in which the given number lies:

1

s

t

Quadrant:

θ

=

α

.

2

n

d

Quadrant:

θ

=

180

−

α

.

3

r

d

Quadrant:

θ

=

α

−

180

.

4

t

h

Quadrant:

θ

=

360

−

α

.

(iv) The polar form of the given complex number is

r

(

cos

θ

+

i

sin

θ

)

Answer and Explanation: