Show that if \( a, b, c, d \in \mathbf{R} \),
\[
\overline{(a+i b)(... VIDEO
Show that if \( a, b, c, d \in \mathbf{R} \),
\[
\overline{(a+i b)(c+i d)}=(a-i b)(c-i d) \text {. }
\]
P
W
📲 PW App Link - https://bit.ly/YTAI_PWAP
🌐 PW Website - https://www.pw.live/
Other Videos By PW Solutions 2023-02-25 FCr any two complex numbers \( z_{1} \) and \( z_{2} \), prove that... 2023-02-25 Solve the following equations :
\[
x^{2}-(3 \sqrt{2}+2 i) x+6 \sqrt... 2023-02-25 Solve the following equations :
\[
x^{2}-(3 \sqrt{2}-2 i) x-6 \sqrt... 2023-02-25 Solve the following equations :
\[
2 x^{2}+3 i x+2=0 \text {. }
\]
... 2023-02-25 Find the reciprocal of :
\[
7+\sqrt{7} i
\]
W 2023-02-25 Find the values of \( x \) and \( y \) if :
\[
\frac{(1+i) x-2 i}{3... 2023-02-25 If \( i z^{3}+z^{2}-z+i=0 \), then show that \( |z|=1 \).
P
W 2023-02-25 If \( x+i y=\sqrt{\frac{a+i b}{c+i d}} \), prove that
\[
\left(x^{2... 2023-02-25 Find the values of \( x \) and \( y \) if :
\[
(x+i y)(1+i)=1-i
\]
... 2023-02-25 If \( z_{1}, z_{2} \) are respectively \( 1-i,-2+4 i \), find \( \m... 2023-02-25 Show that if \( a, b, c, d \in \mathbf{R} \),
\[
\overline{(a+i b)(... 2023-02-25 If \( 1+4 \sqrt{3} i=(a+i b)^{2} \), prove that :
\[
a^{2}-b^{2}=1 ... 2023-02-25 Find the sum and product of the complex numbers :
\[
-\sqrt{3}+\sqr... 2023-02-25 Prove that :
\( z=-\bar{z} \) iff \( z \) is either zero or purely ... 2023-02-25 Let \( z_{1}=2-3 i \) and \( z_{2}=5+12 i \), verify that
\[
\there... 2023-02-25 Find the reciprocal of :
\[
7+\sqrt{7} i
\]
W 2023-02-25 Find the reciprocal of :
\[
i-5
\]
P 2023-02-25 Perform the following by the indicated operations. Express the resu... 2023-02-25 Compute: \( \quad \sqrt{-49}(2+\sqrt{-9}) \)
P
W 2023-02-25 Show that \( (-\sqrt{-1})^{4 n+3}=i \), where \( n \) is a positive... 2023-02-25 Prrform the following by the indicated operations. Express the resu...