Exercise · ZW-COMPLEX-CONJUGATE-007 · ★★☆ Intermediate
If \(z=1+2i\), compute \((\bar z)^2\).
Choose one option.
Show answer
- D. \(-3-4i\)
Explanation
\(\bar z=1-2i\) and \((1-2i)^2=1-4i+4i^2=-3-4i\). It is the conjugate of \(z^2=-3+4i\).
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-008 Find the complex number z with z+2bar z=6-3i.
- ZW-COMPLEX-CONJUGATE-009 For which complex numbers does z=bar z hold?