The value of 6[cos50^∘+i sin50^∘] ÷3(cos20^∘+i sin20^∘) in polar form is (a) 2(cos30^∘+i sin30^∘

step 1 So in the given question we are told to find the value of an expression that is given as 6 times

The value of 6[cos50^∘+i sin50^∘] ÷3(cos20^∘+i sin20^∘) in...

The value of $6\left[\cos 50^{\circ}+\mathrm{i} \sin 50^{\circ}\right] \div 3\left(\cos 20^{\circ}+\mathrm{i} \sin 20^{\circ}\right)$ in polar form is (a) $2\left(\cos 30^{\circ}+\mathrm{i} \sin 30^{\circ}\right)$ (b) $5\left(\cos 30^{\circ}+i \sin 30^{\circ}\right)$ (c) $2\left(\cos 30^{\circ}-\mathrm{i} \sin 30^{\circ}\right)$ (d) $3\left(\cos 70^{\circ}+i \sin 70^{\circ}\right)$

The value of $6\left[\cos 50^{\circ}+\mathrm{i} \sin 50^{\circ}\right] \div 3\left(\cos 20^{\circ}+\mathrm{i} \sin 20^{\circ}\right)$ in polar form is
(a) $2\left(\cos 30^{\circ}+\mathrm{i} \sin 30^{\circ}\right)$
(b) $5\left(\cos 30^{\circ}+i \sin 30^{\circ}\right)$
(c) $2\left(\cos 30^{\circ}-\mathrm{i} \sin 30^{\circ}\right)$
(d) $3\left(\cos 70^{\circ}+i \sin 70^{\circ}\right)$

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Key Concepts

Polar Representation of Complex Numbers

This concept involves expressing complex numbers in the form r(cos ? + i sin ?), where r is the modulus (or absolute value) and ? is the argument (or angle). It provides a geometric interpretation on the complex plane, making it easier to perform multiplication and division, as these operations translate into operations on the moduli and the angles.

Division of Complex Numbers in Polar Form

When dividing two complex numbers represented in polar form, the process involves dividing their moduli and subtracting the angle of the denominator from the angle of the numerator. This operation simplifies the division process by dealing directly with the magnitude and direction of the numbers, rather than their real and imaginary components.

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