Evaluate the following complex numbers and leave your results in polar form: (a) 5∠30∘(6−j8+5∠60∘2+j) (b) (10∠60∘)(35∠−50∘)(2+j6)−(5+j)

Question

Evaluate the following complex numbers and leave your results in polar form: (a) 5∠30∘(6−j8+5∠60∘2+j)  (b) (10∠60∘)(35∠−50∘)(2+j6)−(5+j)

Stephanie Mann · Accepted Answer

Step 1&amp;nbsp;As a general rule, complex numbers are added or subtracted in rectangle form, whereas multiplication and division are accomplished in polar form.(a)&amp;nbsp;5∠30∘(6−j8+3∠60∘2+j)=5∠30∘(6−j8+3∠60∘2.236∠26.565∘)&amp;nbsp;=5∠30∘(6−j8+1.3416∠33.43∘)&amp;nbsp;=5∠30∘(6−j8+1.1196+j0.7392)&amp;nbsp;=5∠30∘(7.13−j7.261)&amp;nbsp;=5∠30∘(10.176∠−45.52∘)&amp;nbsp;=50.88∠−15.52∘&amp;nbsp;Step 2&amp;nbsp;(b)&amp;nbsp;(10∠60∘)(35∠60∘)(2+j6)−(5+j)=(10∠60∘)(35∠−50∘)−3+j5&amp;nbsp;=(10∠60∘)(35∠−50∘)5.83∠120.96∘&amp;nbsp;=60.02∠−110.96∘

Lauren Fuller · Accepted Answer

a) (5∠30∘)(6−j8+1.1197+j0.7392)=(5∠30∘)(7.13−j7.261)  =(5∠30∘)(10.176∠−45.52∘)=50.88∠−15.52∘  b) (10∠60∘)(35∠−50∘)(−2+j5)=(5.83∠120.96∘)=60.02∠−110.96∘

Evaluate the following complex numbers and leave your results in

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