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The value of \((z+3)(\overline{z}+3) \) is equivalent to______
( Given)
Let
Write locus of \( z \), if \(\left \dfrac{z2}{z+2} \right=\dfrac{\pi}{6} \).
i.e., , which is a circle.
(where ), locus of is a circle.
If \( z=4\) and \( \arg (z)=\dfrac{5\pi}{6}\), then \( z \) is______
and
Complex conjugate of \(\dfrac{2i}{(12i)^2} \) is_____
If \( z=2\) and \(\arg (z)=\dfrac{\pi}{3} \) then \( z \) is equal to_____
and
Let
and
Conjugate of \( \dfrac{1+2i}{1i}\) lies in____
Hence lies in quadrant.
Conjugate of \(1i \) lies in_____
Hence, lies in quadrant
If \( \dfrac{(a^2+1)^2}{2a1}=x+iy\), then what is the value of \( x^2+y^2\)?
Find the value of \( \left (1+i)\dfrac{(2+i)}{(3+i)} \right\)
Find the principal argument of \( (1+i \sqrt{3})^2\)
< and > lines in quadrant.
Where does \( z \) lie, if \(\left \dfrac{z5i}{z+5i} \right=1 \)
lies on a real axis.
If \( x,y \in R\), then \( x+iy\) is a nonreal complex number if,______
is nonreal complex number iff .
If \( a+ib=c+id\), then_______
If \( z=x+iy\) lies in \( 3 \text { rd}\) quadrant, then \( \dfrac{\overline{z}}{z}\) also lies in the \( 3 \text { rd}\) quadrant if_____
lies in the quadrant < and <
Since also lies in quadrant.
< and <
< and <
< and <
< and <
< <
The value of \( (z+7)(\overline{z}+7)\) is equivalent to ________
If \(\left( \dfrac{1+i}{1i} \right)^x=1 \), then_____
Which of the following is correct for any two complex numbers \( z_1\) and \(z_2\)
And
The point represented by the complex number \( (2i)\) is rotated about origin through an angle \(\dfrac{\pi}{2} \) in the clockwise direction, the new position is_____
It is rotated about origin through an angle in clockwise direction .
The value of \( \arg (x)\), when \(x \) < \(0 \) is______
and <
Since, the point represent lies on the negative side of real axis.
If \( f(z)=\dfrac{7z}{1z^2}\), where \(z=1+2i \), then \( f(z)\) ie equal to______
Let
If \(\arg (z1)=\arg (z+3i) \), then find \(x1:y \), where \( z=x+iy\)
Solve: \(x=\sqrt{100}\times \sqrt{64} \)
Solve: \(\dfrac{1i}{2+i} \) in \(x+iy \) form.
If \(z=x+iy \), then_____
If \( z=x+iy\), then______