Express ` sin 30^0+i cos 30^0 ` in polar form

Express the fractions in their simplest forms: 30/(54)

The valiue of sin60^(@) cos 30^(@) + sin 30^(@)cos 60^(@) is ______.

Evaluate : [{:(,4 sin 30^@ 2 cos 60^@), (,sin 90^@ 2 cos 0^@):}] [{:(,4,5),(,5,4):}]

if a=cos 0 + i sin 0,=cos 20 -i sin 20, c= cos3 0 + I sin 3 0 and if |{:(a,,b,,c),(b,,c,,a),(c,,a,,b):}| =0 then

If x tan 45^@ sin 30^@ = cos 30^@ tan 30^@ , then x is equal to

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)

Find the modulus and argument of the following complex number and hence express them in the polar form: sin 120^@-i\ cos 120^@

Prove that : (i) sin 60^(@) = 2 sin 30^(@) cos 30^(@) (ii) 4(sin^(4) 30^(@) + cos^(4) 60^(@)) - 3(cos^(2)45 - sin^(2)90^(@)) = 2