Express the following complex numbers in rectangular form. show how you get the answer and use a calculator to verify your answer. e. g. 2 pts for 2∠30°=2(cos30°+°)=1.73+; 1 pt for 2∠30°=1.73+ same grading criteria as 1.4. (a) =° (b) =−3 ∠(−45°) (c) =2∠(−90°)

the question is incomplete, below is the complete question

"ress the following complex numbers in rectangular form. Show how you get the answer and use a calculator to verify your answer. E.g. 2 pts for 2∠30°=2(cos30°+jsin30°)=1.73+j, 1 pt for 2∠30°=1.73+j. Same grading criteria as 1.4. (a) Z1=5eⁱ³⁰ (b) z2=−3 ∠(−45°) (c) z3=2∠(−90°)

answer

a.Z1=4.33+j2.5

b. Z2=-2.12+j2.12

c.Z3=-2j

Step-by-step explanation

note that

Z=reⁱⁿ=r(cosπ+jsinπ)

hence from Z1=5eⁱ³⁰ wen have

Z1=5(cos30+jsin30)

Z1=5(0.8660+j0.5)

Z1=4.33+j2.5

b.also from z=r∠(π)=r(cosπ+jsinπ)

Hence,

z2=−3 ∠(−45°)=-3(cos(-45)+jsin(-45))

Z2=-3(0.7071-j0.7071)

Z2=-2.12+j2.12

c. z3=2∠(−90°)=2(cos(-90)+jsin(-90))

Z3=2(0-j)

Z3=-2j

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.

a is the right answer