Subtracting complex in polar

Given w =√2(cosine (pi/4) + i sine (pi/4) ) and z = 2 (cosine (pi/2) + i sine (pi/2) ).

What is w - z expressed in polar form?

Final Answer:

m =  1.4142
A =  -0.7854 rad

Step-by-step explanation:

wx​=2​⋅ cos(π/4)=2​⋅ cos(3.1416/4)=1 wy​=2​⋅ sin(π/4)=2​⋅ sin(3.1416/4)=1  zx​=2⋅ cos(π/2)=2⋅ cos(3.1416/2)=1.2246⋅10−16 zy​=2⋅ sin(π/2)=2⋅ sin(3.1416/2)=2  x=wx​−zx​=1−1.2246⋅10−16=1 y=wy​−zy​=1−2=−1  m=x2+y2​=12+(−1)2​=2​=1.4142
A=arctan(y/x)=arctan((−1)/1)≐−0.7854 rad  α=A→  °=A⋅ π180​   °=(−0.7854)⋅ π180​   °=−45  °

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arithmeticplanimetricsnumbersgoniometry and trigonometryUnits of physical quantitiesGrade of the word problem

 
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