9514 1404 393
Answer:
45. (8√2)∠π/4
46. (7√2)∠3π/4
Step-by-step explanation:
The polar form of a+bi is ...
a +bi ⇔ (√(a²+b²))∠arctan(b/a)
__
45. 8 +8i = (√(8² +8²))∠arctan(8/8) = (8√2)∠π/4
__
46. -7 +7i = (√((-7)² +7²))∠arctan(7/-7) = (7√2)∠3π/4
_____
Additional comment
The arctan function usually returns a value in the range -π/2 to π/2. The quadrant of the desired result can be determined by the signs of the components of the vector. For negative real parts, π needs to be added to the value that is usually returned by the arctan function.
