Question

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°+????sin30°)=1.73+????; 1 pt for 2∠30°=1.73+????. Same grading criteria as 1.4. (a) ????1=5????????30° (b) ????2=−3 ∠(−45°) (c) ????3=2∠(−90°)

Answer 1

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

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