Answer : $\;n \pi , n \in Z$Explanation :$\;\large\frac{3 +2i sin \theta}{1-2isin\theta}\;= \large\...

Answer : $\;1$Explanation :We have , $\;x+iy = \large\frac{a+ib}{a-ib}\; $$= \large\frac{a+ib}{a-i...

Answer : $\;\large\frac{1}{\sqrt{2}} , -\large\frac{\pi}{4}$Explanation :We have , $\; \large\frac...

Answer : $\;1 , \large\frac{\pi}{2}$Explanation :We have , $\; \large\frac{1+i}{1-i}$$ \large\fr...

Answer : $\;\large\frac{63}{25}+ \large\frac{16}{25}i$Explanation :We have , $\;\large\frac{(3-2i...

Answer : $\;\large\frac{-1\pm\sqrt{19}i}{2\sqrt{5}}$Explanation : $\; \sqrt{5} x^{2} + x + \sqrt{...

Answer : $\;\large\frac{-1\pm \sqrt{3}i}{2}$Explanation :we have , $\;x^{2} + x + 1=0 $$b^{2} - 4a...

Answer : $\;\pm \sqrt{2} i$Explanation :we , have $\;x^{2}+2 =0 \;$$x^{2} = -2$i.e $\; x = \pm \sq...

Answer : $\;8(cos \large\frac{2\pi}{3}+ i sin\large\frac{2\pi}{3})$Explanation :the complex given ...

Answer : $\;2(cos \large\frac{\pi}{3}+ i sin\large\frac{\pi}{3})$Explanation :Let $\; r cos \theta...

Answer : $\;i$Explanation :$ i^{-35} = \large\frac{1}{i^{35}} = \large\frac{1}{(i^{2})^{17} i}$$=...

Answer : $\;1+2\sqrt{2} i$Explanation :$\large\frac{5 + \sqrt{2} i }{1 - \sqrt{2} i}= \large\frac{5...

Answer : $\;\large\frac{2}{13}+ i \large\frac{3}{13}$Explanation :Let $\;z=2-3i\;$ then $\;\overlin...

Answer : $\;(-6+\sqrt{2})+\sqrt{3}(1+2\sqrt{2}) i$Explanation :$\;(- \sqrt{3} + \sqrt{-2})(2 \sqrt...

Answer : $\;-10-198i$Explanation :We have , $\;(5-3i)^{3}\; = 5^{3}-3 \times 5^{2} \times (3i) +...

Answer : $\;\large\frac{1}{256} i$Explanation :$(-i) \; (2i)\;(-\large\frac{1}{8}i)^{3}= 2 \times...

Answer : $\;\large\frac{5}{8} + 0 i $Explanation :$(-5i) \; (\large\frac{1}{8}i) = \large\frac{5}...

Answer : $\;\large\frac{3}{4} , \large\frac{33}{4}$Explanation :$\;4x+i(3x-y)=3+i (-6)\;$----(1)Equ...

Answer : $\;Rez_{1}Rez_{2} - Imz_{1}Imz_{2}$Explanation :Let $\;z_{1}=x_{1}+iy_{1}\;$ and $\;z_{2}...

Answer : 4Explanation :$\;(\large\frac{1+i}{1-i})^{m}=1\; $$ (\large\frac{1+i}{1-i} \times \large\...

Answer : $\;A^{2}+B^{2}$Explanation :$\;(a^{2}+b^{2})(c^{2}+d^{2})(e^{2}+f^{2})(g^{2}+h^{2}) = A^{...

Answer : 0Explanation :$\;|1-i|^{x}=2^{x}$$(\sqrt{1^{2}+(-1)^{2}})^{x} = 2^{x}$$(\sqrt{2})^{x} =2^...

Answer : 1Explanation :Let $\; \alpha = a+ib\;$ and $\; \beta = x+iy$It is given that $\;|\beta|...

Answer : $\;4(x^{2}-y^{2})$Explanation :$\;(x+iy)^{3}=u+iv\;$$x^{3}+(iy)^{3}+3\;.x\;.(iy) (x+iy) =u...

Answer : $\;2$Explanation :$\;\large\frac{1+i}{1-i} - \large\frac{1-i}{1+i} = \large\frac{(1+i)^{2...

Answer : $\;3 ,-3$Explanation :Let $\;z= (x-iy)(3+5i)\;= 3x+5xi-3iy-5yi^{2}$$= 3x + 5y+5xi-3iy$$= (...

Answer : $\;\large\frac{1}{\sqrt{2}}\;and\;\large\frac{3 \pi}{4}$Explanation :Let $\;z=\large\frac...

Answer : $\;-\large\frac{2}{5},0$Explanation :$\;z_{1}=2-i\;,z_{2}=-2+i\;$(i) $\;z_{1}z_{2}= (2-i)(...

Answer : D.I.MendeleefPeriodic is based on the laws found out by D.I.Mendeleef

Answer : $\;1 : 3$The base radius of a right circular cone and those of a cylinder are same . Their ...

Answer : $\;\alpha\;rays$Ionizing power is more for $\;\alpha\;rays$

Answer : SpeakerHead of Lok Sabha is Speaker

Answer : Oxidation takes placeAnode is a terminal Oxidation takes place

Answer : Calcium OxychlorideBleaching powder is chemically known as Calcium Oxychloride

Answer : $\;30\;m$A man observes the top of a building with an angle of elevation $\;45^{0}\;$ from...

Answer : $\;40$then angle SCB is 40

Answer : Boiling point of water decreases due to pressureIn a pressure cooker food is cooked faster...

Answer : Wavelength is long so it travels longer unscattered and it is visible from long distanceRe...

Answer : ovaryAfter fertilization the part of a flower that develops as fruit is ovary

Answer : Kidney are affectedDialysis is the procedure for patients - Kidney are affected

Answer : Pulmonary veinPulmonary vein is different from the others in one aspect

Answer : excretory systemOsmoregulation in our body is governed by excretory system

Answer : digestive systemAlimentary canal is associated with digestive system .

Answer : $\;2.4092\times10^{25}$Number of atoms present in 40 gram of $\;(_{1}H^{1})_{2}\;$ gas is ...

Answer : imaginaryThe roots of the equation $\;3x^{2}-2x+3=0\;$ are imaginary .

Answer : 44 common tangents that can be drawn for two non intersecting circles with two different c...

Answer : $\;CH_{4}$Green house effect is caused by - $\;CH_{4}$

Answer : IR raysHeat radiations are IR rays

Answer : All the aboveFuse wire of a household circuit melts because of - Overloading , Short circu...

Answer : $\;19.6\;ms^{-1}$A stone is dropped from a rising balloon at a height of 300 m above the g...