Find squareroot 3 i6 and write the answer in standard form

Find (- squareroot 3 + i)^6 and write the answer in standard form. 64 - 64 squareroot 3 i -64 squareroot 3 + 64 i 64 i -64 Given vectors u = -10 i - 2j and v = 8i + 7j; Find u-0v. -20 i + 5j -19 i + 5j -2i + 5j -18 i - 9j u = -8i - 2j, v = -2i + 9; Find u + v. -11i + 7j -6i - 11j 6i + 7j -10i + 7j u = 10 i - 2j, v = -8i + 7j; Find u - v. 17i + 5j 16i + 5j 18 i - 9j 2i + 5j Find the magnitude of the vector y = 2 i + 4 j 2 squareroot 6 2 squareroot 5 6 Write the complex number z = 3(cos pi/3 + i sin pi/3) In rectangular form. squareroot 3/2 + 3 squareroot 3/2 i 3/2 + 3 squareroot/2 i squareroot 3/6 + squareroot 3/6 i squareroot 3 + i Use the given vectors to find the specified dot product: u = 8i + 4j; v = 9i - -16 56 72 88

Solution

24.     (-sqrt3 + i)⁶

R=sqrt(3+1)=2

theta=tan^-1(-1/sqrt3)= 5pi/6

Therefore (-sqrt3 + i)⁶=(2(cos 5pi/6 + i sin 5pi/6)⁾⁶= 2⁶(cos (6*5pi/6) + i sin(6* 5pi/6))

                                                                                     =64(-1+0i)

                                                                                     =-64

25. u=-10i-2j    v=8i+7j

u-v= -10i -2j-8i-7j =-18i -9j