Question

The polar form of the complex number 2i/3e4+i

Answer 1

we have to write the complex number $\frac{2i}{3e^{4+i}}$ in the polar form.

solution : The polar form of a complex number is given as $re^{i\theta}$ where r is modulus of complex and θ is argument.

now here, complex number is $\frac{2i}{3e^{4+i}}$

numerator is 2i [ an imaginary number ]

Modulus, r = √(0² + 2²) = 2

argument, θ = π/2

so, polar form of numerator is $2e^{i\frac{\pi}{2}}$

now complex number in polar form is ..

$\frac{2e^{i\frac{\pi}{2}}}{3e^{4+i}}$

= $\frac{2}{3e^4}e^{i\left(\frac{\pi}{2}-1\right)}$

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