Evaluate the following complex numbers and leave your results in

deliredejoker7m 2021-11-23 Answered
Evaluate the following complex numbers and leave your results in polar form: (a) \(\displaystyle{5}\angle{30}^{{\circ}}{\left({6}-{j}{8}+{\frac{{{5}\angle{60}^{{\circ}}}}{{{2}+{j}}}}\right)}\)
(b) \(\displaystyle{\frac{{{\left({10}\angle{60}^{{\circ}}\right)}{\left({35}\angle-{50}^{{\circ}}\right)}}}{{{\left({2}+{j}{6}\right)}-{\left({5}+{j}\right)}}}}\)

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Stephanie Mann
Answered 2021-11-24 Author has 8218 answers
Step 1
As a rule of thumb, if we add or subtract complex numbers, we will do that in rectangular form while multiplication, divison will be performed in polar form.
(a) \(\displaystyle{5}\angle{30}^{{\circ}}{\left({6}-{j}{8}+{\frac{{{3}\angle{60}^{{\circ}}}}{{{2}+{j}}}}\right)}={5}\angle{30}^{{\circ}}{\left({6}-{j}{8}+{\frac{{{3}\angle{60}^{{\circ}}}}{{{2.236}\angle{26.565}^{{\circ}}}}}\right)}\)
\(\displaystyle={5}\angle{30}^{{\circ}}{\left({6}-{j}{8}+{1.3416}\angle{33.43}^{{\circ}}\right)}\)
\(\displaystyle={5}\angle{30}^{{\circ}}{\left({6}-{j}{8}+{1.1196}+{j}{0.7392}\right)}\)
\(\displaystyle={5}\angle{30}^{{\circ}}{\left({7.13}-{j}{7.261}\right)}\)
\(\displaystyle={5}\angle{30}^{{\circ}}{\left({10.176}\angle-{45.52}^{{\circ}}\right)}\)
\(\displaystyle={50.88}\angle-{15.52}^{{\circ}}\)
Step 2
(b) \(\displaystyle{\frac{{{\left({10}\angle{60}^{{\circ}}\right)}{\left({35}\angle{60}^{{\circ}}\right)}}}{{{\left({2}+{j}{6}\right)}-{\left({5}+{j}\right)}}}}={\frac{{{\left({10}\angle{60}^{{\circ}}\right)}{\left({35}\angle-{50}^{{\circ}}\right)}}}{{-{3}+{j}{5}}}}\)
\(\displaystyle={\frac{{{\left({10}\angle{60}^{{\circ}}\right)}{\left({35}\angle-{50}^{{\circ}}\right)}}}{{{5.83}\angle{120.96}^{{\circ}}}}}\)
\(\displaystyle={60.02}\angle-{110.96}^{{\circ}}\)
Not exactly what you’re looking for?
Ask My Question
0
 
Lauren Fuller
Answered 2021-11-25 Author has 7525 answers
a) \(\displaystyle{\left({5}\angle{30}^{{\circ}}\right)}{\left({6}-{j}{8}+{1.1197}+{j}{0.7392}\right)}={\left({5}\angle{30}^{{\circ}}\right)}{\left({7.13}-{j}{7.261}\right)}\)
\(\displaystyle={\left({5}\angle{30}^{{\circ}}\right)}{\left({10.176}\angle-{45.52}^{{\circ}}\right)}={50.88}\angle-{15.52}^{{\circ}}\)
b) \(\displaystyle{\frac{{{\left({10}\angle{60}^{{\circ}}\right)}{\left({35}\angle-{50}^{{\circ}}\right)}}}{{{\left(-{2}+{j}{5}\right)}={\left({5.83}\angle{120.96}^{{\circ}}\right)}}}}={60.02}\angle-{110.96}^{{\circ}}\)
0

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-08-12
Two college friends are taking a weekend road trip. Friday they leave home and drive 87 miles north for a night of dinner and dancing in the city. The next morning they drive 116 miles east to spend a day at the beach. If they drive straight home from the beach the next day, how far do they have to travel on Sunday?
asked 2021-12-31
Find the product of the complex numbers.Leave answers in polar form.
\(\displaystyle{z}_{{{1}}}={1}+{i}\)
\(\displaystyle{z}_{{{2}}}=-{1}+{i}\)
asked 2021-12-20
Find the product of the complex numbers \(\displaystyle{z}_{{{1}}}={\cos{{\frac{{\pi}}{{{6}}}}}}+{i}{\sin{{\frac{{\pi}}{{{6}}}}}}\) and \(\displaystyle{z}_{{{2}}}={\cos{{\frac{{\pi}}{{{4}}}}}}+{i}{\sin{{\frac{{\pi}}{{{4}}}}}}\)
Leave answer in polar form.
asked 2021-09-13
Find all the complex roots. Leave your answers in polar form with the argument in degrees. The complex fourth roots of \(\displaystyle{100}+{100}\sqrt{{3}}{i}\)
asked 2021-11-18
Find each measurement indicated. Round your answers to the nearest tenth.
Find BC
asked 2021-08-15
Tell whether two angles can be as described. Justify your answers.
a. vertical and complementary
b. vertical and supplementary
c. complementary and supplementary
asked 2021-11-29
Solve each of the following triangles. If there are two triangles, solve both. Round angle measurements to one decimal place and side lengths to two decimal places. \(\displaystyle{a}={9},{b}={4},{B}={23}^{{\circ}}\)
a=
y=
c=
...