CONVERTING FROM POLAR FORM TO RECTANGULAR FORM

Convert the following polar form to rectangular form.

Problem 1 :

Solution :

= 4 [cos (7𝜋/6) + i sin (7𝜋/6)]

Here 𝜃 lies in the third quadrant. Using ASTC, since it lies in the third quadrant, we use negative sign.

Applying the values in the respective places in the polar form, we get

Problem 2 :

Solution :

Here 𝜃 lies in the first quadrant. Using ASTC, we have to use positive sign.

applying the values in the respective places in the given polar form, we get

= 2√7(√3/2 + i(1/2))

= 2√7(√3 + 1i) / 2)

= √7(√3 + 1i)

Distributing √7, we get

= (√21 + i√7)

Problem 3 :

Solution :

Here 𝜃 lies in the third quadrant. Using ASTC, we have to use negative sign for both.

Problem 4 :

Solution :

Applying the values in the respective places, we get

Problem 5 :

Solution :

Applying the values in the respective places, we get

Problem 6 :

Solution :

Here 𝜃 lies in the third quadrant. Using ASTC, we have to use negative sign for both.

applying the values in the respective places in the given polar form, we get

= 2(-1/2 + i(-√3/2))

= 2((-1 - i√3) / 2)

= (-1 - i√3)

Problem 7 :

Solution :

Here 𝜃 lies in the first quadrant. Using ASTC, we have to use positive sign for both.

applying the values in the respective places in the given polar form, we get

= 2(√3/2 + i(1/2))

= 2((√3 + i) / 2)

= √3 + i

Problem 8 :

√30(cos 𝜋 + i sin 𝜋)

Solution :

cos 𝜋 = -1 and sin 𝜋 = 0

Applying these values in the respective places, we get

= √30((-1) + i (0))

= -√30