Exercise · ZW-COMPLEX-NUMBER-010 · ★★★ Advanced
Compute \(\left(\dfrac{1+i}{1-i}\right)^3\).
Choose one option.
Show answer
- B. \(-i\)
Explanation
\(\frac{1+i}{1-i}=\frac{(1+i)^2}{2}=\frac{2i}{2}=i\), and \(i^3=-i\).
Review the concept: Complex number
A complex number \(z\) is written with two reals, \(a\) and \(b\), and the imaginary unit \(i\), which satisfies \(i^2=-1\); \(a\) is its real part and \(b\) its imaginary part.
\[z=a+bi,\qquad a=\operatorname{Re}z,\ b=\operatorname{Im}z,\qquad i^2=-1\]
More practice problems: complex number
- ZW-COMPLEX-NUMBER-001 Compute (2+3i)+(1-5i).
- ZW-COMPLEX-NUMBER-002 Compute (1+2i)(3-i).
- ZW-COMPLEX-NUMBER-003 What is the imaginary part of 4-7i?
- ZW-COMPLEX-NUMBER-004 Compute i^2026.
- ZW-COMPLEX-NUMBER-005 Write (1)/(1+i) in the form a+bi.
- ZW-COMPLEX-NUMBER-006 Compute (3+4i)^2.
- ZW-COMPLEX-NUMBER-007 Find all complex solutions of z^2+4=0.
- ZW-COMPLEX-NUMBER-008 Compute (1+i)^4.