Question
Let $z=a+b i$ and $w=c+d i$(a) Show that $\overline{\bar{z}}=z$(b) Show that $\overline{(z+w)}=\bar{z}+\bar{w}$
Step 1
So, the conjugate of $\bar{z}$ is $\overline{\bar{z}}=a-(-b)i=a+bi=z$. Hence, we have shown that $\overline{\bar{z}}=z$. Show more…
Show all steps
Your feedback will help us improve your experience
Rakesh Kumar Sharma and 83 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Use $z=a+b i$ and $w=c+d i$ to show that $\bar{z}+w=\bar{z}+\bar{w} .$
Equations and Inequalities
Complex Numbers; Quadratic Equations in the Complex Number System
Let $z=a+b i$ (a) Show that $(\bar{z})^{2}=\overline{z^{2}}$ (b) Show that $(\bar{z})^{3}=\overline{z^{3}}$
Roots of Polynomial Equations
The Complex Number System
Use $z=a+b i$ to show that $z+\bar{z}=2 a$ and $z-\bar{z}=2 b i$
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD