List of practice Questions

Express the given complex number in the form \(a + ib: i^{-39}\)
Express the given complex number in the form \(a + ib: 3(7 + i7) + i(7 + i7)\)

Express the given complex number in the form \(a + ib: (\dfrac{1}{5}+i\dfrac{2}{5})-(4+i\dfrac{5}{2})\)

 

 

Express the given complex number in the form \(a + ib: [(\dfrac{1}{3}+i\dfrac{7}{3})+(4+i\dfrac{1}{3})]-(-\dfrac{4}{3}+i)\)
Express the given complex number in the form \(a + ib: (1 - i)^{4}\)
Express the given complex number in the form \(a + ib: (\dfrac{1}{3}+3i)^3\)
Express the given complex number in the form\( a + ib: (-2-\dfrac{1}{3}i)^3\)
Find the multiplicative inverse of the complex number \( 4 - 3i\)
Find the multiplicative inverse of the complex number \(√5+3i\)\(\)

Find the multiplicative inverse of the complex number \(-i\)

Express the following expression in the form of a + ib.

\(\dfrac{(3+i√5)(3-i√5)}{(√3+√2i)-(√3-i√2)}\)

Reduce  \((\frac{1}{1-4i}-\frac{2}{1+i})(\frac{3-4i}{5+i})\) to the standard form .

\(if\, x-iy=√\frac{a-ib}{c-id}\) prove that \((x^2y^2)^2=\frac{a^2+b^2}{c^2+d^2}.\)
\(if\, x-iy=√\frac{a-ib}{c-id}\) prove that \((x^2y^2)^2=\frac{a^2+b^2}{c^2+d^2}.\)
\(If \,z_1=2-i,z_2=1+i, find \,|\frac{z_1+z_2+1}{z1-z2+1}|.\)
\(If a + ib =\frac{(x+1)^2}{2x^2+1},\,prove\, that\, a^2 + b^2 =\frac{(x^2+1)^2}{(2x^2+1)}\)
\(Let\, z_1=2 – i,z_2 = –2+i.\, Find\, (i) Re(\frac{z_1z_2}{z_1}), (ii) \,Im(\frac{1}{z_1z_1})\)
Find the modulus of \(\frac{1+i}{1+i}-\frac{1-i}{1+i}.\)
If \((x+iy) ^3=u+iv,\) then show that \(\frac{u}{x}+\frac{v}{y}=4(x^2-y^2).\)
If α and β are different complex numbers with |β|=1, then find \(| \frac{β-α}{1-\bar{α}β} |.\)
\(\text{Find the number of non-zero integral solutions of the equation }|1-i|^x=2^2.\)
\(If (a+ib) (c+id) (e+if)(g+ih)=A+iB, \text {then show that} (a^2+b^2 )(c^2+d^2) (e^2+f^2)(g^2+h^2)=A^2+B^2.\)
\(If (\frac{(1+i}{1-i})^m=1, \text{then find the least positive integral value of m.}\)