Write -1- i -3 in polar form-

Let z = 1 + i √(3) Modulus, |z|=√(( 1)^2+(√(3))^2)=√(4)=2 Argument, θ=tan^ 1(√(3)/1)=tan^ 1( √(3)) =π π/3=2π/3 Polar Form,2[cos(2π/3 )+i sin(2π/3 ) ]=2 [cos ...

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Standard XII

Mathematics

Algebra of Complex Numbers

Write -1+ i √...

Question

Write -1 + i $\sqrt{3}$ in polar form.

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Solution

Let z = -1 + i $\sqrt{3}$

$Modulus, | z | = \sqrt{(- 1)^{2} + (\sqrt{3})^{2}} = \sqrt{4} = 2 A r g u m e n t, θ = t a n^{- 1} (\frac{\sqrt{3}}{1}) = t a n^{- 1} (- \sqrt{3}) = π - \frac{π}{3} = \frac{2 π}{3} Polar Form, 2 [c o s (\frac{2 π}{3}) + i s i n (\frac{2 π}{3})] = 2 [c o s (\frac{2 π}{3}) + i s i n (\frac{2 π}{3})]$

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Write -1 + i √3 in polar form.

Let z = -1 + i √3 Modulus, |z|=√(−1)2+(√3)2=√4=2Argument, θ=tan−1(√31)=tan−1(−√3)=π−π3=2π3Polar Form,2[cos(2π3)+i sin(2π3)]=2[cos(2π3)+i sin(2π3)]

Write -1 + i $\sqrt{3}$ in polar form.