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b 15 - 4i sqrt(2)

Step-by-step explanation:

15 - sqrt (-32)

15 - sqrt(-1) sqrt(32)

15 - ±i sqrt(16) sqrt(2)

15 - ±4i sqrt(2)

Taking the principal square root

15 - 4i sqrt( 2)

15 - √-32

Rewrite √-32 as √-1 * √32

√-1 = i

Now you have 15 - i * √32

Rewrite √32 as √(4^2 * 2)

Pull terms out from under the radical:

15 - i * 4√2

Multiply i by 4 to get final answer of 15 - 4i√2

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this