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

Evaluate (1+i)10.

1. 32
2. -32i
3. 32i
4. 1024i

Answer

C. 32i

Solution

1+i= 2, cis,45°. By De Moivre's theorem, (1+i)10=( 2)10, cis,450°=32, cis,90°=32i.

More Complex Numbers: Polar and Exponential Form questions

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