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

Find all fourth roots of -16.

1. 2, 2i
2. 1 i
3. 2 2,i
4. 2 2i

Answer

C. 2 2,i

Solution

-16=16, cis,180°, so the roots are 2, cis,180°+360° k/4 for k=0,1,2,3: angles 45°,135°,225°,315°. Each root is 2( 2/2 2/2i)= 2 2,i.

More Complex Numbers: Polar and Exponential Form questions

1. Write 1+i 3/1-i in polar form.
2. Find the product (2, cis,40°)(3, cis,80°).
3. Simplify ( 15°+i 15°)8.
4. Evaluate (1+i)10.
5. Evaluate eiπ.
6. Write -1+i in polar form.
7. Write 4+4i in polar form.
8. Convert 10 60° to rectangular form.
9. Find the polar form of -3+3i.
10. Multiply using polar form: (2, cis,30°)(3, cis,60°)

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