Exercise · ZW-COMPLEX-CONJUGATE-009 · ★★★ Advanced
For which complex numbers does \(z=\bar z\) hold?
Choose one option.
Show answer
- C. Exactly the real numbers.
Explanation
\(a+bi=a-bi\) is equivalent to \(b=0\), i.e. \(z\) is real.
Review the concept: Complex conjugate
The conjugate of a complex number \(z\), with real part \(a\) and imaginary part \(b\), is the complex number \(\bar z\) that keeps the real part and flips the sign of the imaginary part.
\[z=a+bi\ \Longrightarrow\ \bar z=a-bi\]
More practice problems: complex conjugate
- ZW-COMPLEX-CONJUGATE-001 Find the conjugate of 3-4i.
- ZW-COMPLEX-CONJUGATE-002 If z=2+3i, compute zbar z.
- ZW-COMPLEX-CONJUGATE-003 If z=5-2i, compute z+bar z.
- ZW-COMPLEX-CONJUGATE-004 If z=2-6i, compute (z-bar z)/(2i).
- ZW-COMPLEX-CONJUGATE-005 Write (1+2i)/(3-i) in the form a+bi.
- ZW-COMPLEX-CONJUGATE-006 Compute overline(1+i)(2-i).
- ZW-COMPLEX-CONJUGATE-007 If z=1+2i, compute (bar z)^2.
- ZW-COMPLEX-CONJUGATE-008 Find the complex number z with z+2bar z=6-3i.