If (1+i)z=(1-i) z , then show that z=-i z . - Vidyadip

Question

If $(1+\text{i})\text{z}=(1-\text{i})\bar{\text{z}},$ then show that $\text{z}=-\text{i}\bar{\text{z}}.$

✓

Answer

$(1+\text{i})\text{z}=(1-\text{i})\bar{\text{z}}$
$\Rightarrow\text{z}=\frac{(1-\text{i})}{(1+\text{i})}\bar{\text{z}}$
$\Rightarrow\text{z}=\frac{(1-\text{i})(1-\text{i})}{(1+\text{i})(1-\text{i})}\bar{\text{z}}$ [Rationalizing the denominator]
$\Rightarrow\text{z}=\frac{(1-2\text{i}-1)}{(1+1)}\bar{\text{z}}$
$\Rightarrow\text{z}=\frac{-2\text{i}}{2}\bar{\text{z}}$
$\Rightarrow\text{z}=-\text{i}\bar{\text{z}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(3 Marks)" from Complex Numbers→Complex Numbers — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

In an A.P., show that $\text{a}_{\text{m}+\text{n}}+\text{a}_{\text{m}-\text{n}}=2\text{a}_\text{m}.$

A cube of side 5 has one vertex at the point(1, 0, -1) and the three edge from this vertex are, respectively, parallel to the negative x and y axes and positive z-axis. Find the coordinates of the other vertices of the cube.

If $\tan\text{A}=\frac{1}{7}$ and $\tan\text{B}=\frac{1}{3},$ show that $\cos2\text{A}=\sin4\text{B}$

A(1, 4), B(2, 3) and C(1, 6) are vertices of AABC. Find the equation of the altitude through B and hence find the co-ordinates of the point where this altitude cuts the side AC of ∆ABC.

Find $\sum_{r=1}^n \frac{1^2+2^2+3^2+\ldots+r^2}{2 r+1}$

If $A=\left[\begin{array}{cc}1 & -2 \\ 3 & -5 \\ -6 & 0\end{array}\right] B=\left[\begin{array}{cc}-1 & -2 \\ 4 & 2 \\ 1 & 5\end{array}\right]$ and $C=\left[\begin{array}{cc}2 & 4 \\ -1 & -4 \\ -3 & 6\end{array}\right]$, find the matrix $X$ such that

3A – 4B + 5X = C.

Find the locus of a point such that the sum of its distances from (0, 2) and (0, -2) is 6.

Find the equation of the ellipse in standard form if
eccentricity $=\frac{3}{8}$ and distance between its foci $=6$.

Find $k$, if the line $3 x+4 y+k=0$ touches $9 x^2+16 y^2=144$.

Discuss the continuity and differentiability of :

f(x) = x |x| at x = 0