Write z 8cos pi6 i sin pi6 in rectangular form 4 squareroo

Write z = 8(cos pi/6 + i sin pi/6) in rectangular form. 4 squareroot3 + 4i 1/4 + squareroot3/4 i 4 + 4 squareroot3 i squareroot 3/4 + 1/4 i Find (squareroot3 + i)^6 and write the answer in standard form. 64 - 64 squareroot3 i -64 squareroot3 + 64i 64i-64 Given vectors u = -10i - 2j and v = 8i + 7j; Find u - v. -20i + 5j -19i +5j -2i + 5j u = -8i - 2j, v = -2i + 9j; Find u + v. -11i + 7j -6i - 11j 6i +7j

Solution

8(cos pi/6 +isin pi/6)

Here R=8 and theta=pi/6

x=R cos theta= 8 cos pi/6=4sqrt3

y=R sin theta=8 sin pi/6=4

Rectangular form is

4sqrt3 + 4i

Correct option is A