30 Please show work Write the expression in the standard for

30 Please show work

Write the expression in the standard form a + bi. [2 (cos 15 degree + i sin 15\')] Select one:

Solution

[2(cos15 +isin15)]^3

= 2^3(cos(15*3) + isin(3*15)

= 8(cos45 +i*sin45)

= 8(1/sqrt2 + i/sqrt2)

rationalising by mulitplying denominator and numerator by sqrt2

So, 8(1/sqrt2 + i/sqrt2) = 8sqrt2(1/2 +i/2)

= 4sqrt2 + i*4sqrt2

Option C