Represent z=1+i√3 in the polar form.

Question

Represent z=1+i√3 in the polar form. (A) cos(π/3)+i sin(π/3) (B) cos (π/3) -isin (π/3) (C) 2(cos (π/3)+isin (π/3)) (D) 4(cos (π/3)+isin (π/3))

Tardigrade Admin · Accepted Answer

Let 1 = r cos θ, √3=rsin θ By squaring and adding, we get r2(cos2 θ+sin2 θ)=4 i.e., r=√4=2 Therefore, cos θ=(1/2), sinθ=(√3/2), which gives θ =(π/3) Therefore, required polar form is z=2(cos(π/3)+i sin(π/3))

Q. Represent $z = 1 + i 3$ in the polar form.

$cos \frac{π}{3} + i s in \frac{π}{3}$

$cos \frac{π}{3} - i s in \frac{π}{3}$

$2 (cos \frac{π}{3} + i s in \frac{π}{3})$

$4 (cos \frac{π}{3} + i s in \frac{π}{3})$

Let $1 = rcos θ, 3 = rs in θ$
By squaring and adding, we get
$r^{2} (co s^{2} θ + s i n^{2} θ) = 4$
i.e., $r = 4 = 2$
Therefore, $cos θ = \frac{1}{2}$ ,
$s in θ = \frac{3}{2}$ ,
which gives $θ = \frac{π}{3}$
Therefore, required polar form is
$z = 2 (cos \frac{π}{3} + i s in \frac{π}{3})$

Q. Represent z=1+i3​ in the polar form.

cos3π​+isin3π​

cos3π​−isin3π​

2(cos3π​+isin3π​)

4(cos3π​+isin3π​)