Write down the following complex number in polar form: ` Product of 2 (cos 30^0+isin 30^0) and 3 (cos 90^0+isin90^0) `

Write down the following complex number in polar form: Quotient of 12 (cos 150^0 + i sin 150^0) and 3(cos 60^0+i sin 60^0)

Change the following complex numbers to Cartesiasn form: 4(cos300^0+isin300^0)

Change the following complex numbers to Cartesiasn form: 5(cos270^0 + i sin 270^0)

Change the following complex numbers to Cartesiasn form: 2(cos0^0+isin0^0)

Give the following products in polar form: [2(cos 210^0+isin210^0)][4(cos120^0+isin120^0)]

Find the modulus and principal argument of the following complex number: 5/2(cos30^0 +isin30^0)

Give the following products in polar form: [3(cos 225^0+i sin225^0)] [6(cos 45^0 + i sin 45^0)]

Give the following quotients in polar form: (9(cos90^0+isin90^0))/(3(cos45^0+isin45^0)

Find the modulus and argument of the following complex number and convert them in polar form: (i-1)/[cos(pi/3)+isin(pi/3)]

Prove that: (cos30^0+sin60^0)/(1+cos60^0+sin30^0)=(sqrt(3))/2