Engineering Board Exam Reviewer · Complex Numbers: Polar and Exponential Form · medium

Simplify ( 15°+i 15°)8.

1. - 12- 3/2i
2. 12+ 3/2i
3. - 3/2+ 12i
4. - 12+ 3/2i

Answer

D. - 12+ 3/2i

Solution

By De Moivre's theorem, ( 15°+i 15°)8= 120°+i 120°=- 12+ 3/2i.

More Complex Numbers: Polar and Exponential Form questions

1. Evaluate (1+i)10.
2. Evaluate eiπ.
3. Write -1+i in polar form.
4. Write 4+4i in polar form.
5. Convert 10 60° to rectangular form.
6. Find the polar form of -3+3i.
7. Multiply using polar form: (2, cis,30°)(3, cis,60°)
8. Divide using polar form: 12, cis,80°4, cis,20°
9. Use De Moivre's Theorem to find (2, cis,30°)3.
10. Evaluate i,i (principal value).

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