Find the conjugate of the complex number \(\frac { 1-i }{ 1+i }\)

Find the conjugate and modulus of the complex number \(\frac { 2+3i }{ 3+2i } \)

Simplify the following
(2i)³

Simplify the following i⁴+i⁸+i¹²+i¹⁶

Find the multiplicative inverse of the following complex number \((2+\sqrt { 3 } i)^{ 2 }\)

Convert the complex number in polar form 1+i tan∝

Express (-3i) (i)\(\left( -\frac { 1 }{ 4 } i \right) ^{ 3 }\) in the form a+ib

Express the following in the form of a + ib.\(\left[ \left( \frac { 1 }{ 3 } +\frac { 7 }{ 3 } i \right) +\left( 4+\frac { 1 }{ 3 } i \right) \right] -\left( -\frac { 4 }{ 3 } +i \right) \)

Express \(\left( -2-5i \right) \div \left( 3-6i \right) \)in the form a+ib

Solve \(2{ x }^{ 2 }-2\sqrt { 3x } +\frac { 21 }{ 8 } =0\) .Compare the given equation with \({ ax }^{ 2 }+bx+c=0\) and use the formula \(x=\frac { -b\pm \sqrt { { b }^{ 2 }-4ac } }{ 2a } \)

Find the modulus and argument of the complex number \(\frac{1+3i}{1-2i}\) and convert them In polar form.

Solve the quadratic equation 5x² - 6x + 2 = 0.

Solve the equation 17x²-8x+1=0

Convert the complex numbers in polar form -1 + i.

If z₁ = 3 + i and z₂ = 1 + 4i, then verify that \(|{ z }_{ 1 }-{ z }_{ 2 }|\ge |{ z }_{ 2 }|-|{ z }_{ 1 }|.\)

If \(|z+1|=z+2(1+i)\) then find z.

Find the value of \({ 2x }^{ 4 }+{ 5x }^{ 3 }+{ 7x }^{ 2 }-x+41,when\ x=-2-\sqrt { 3i } \)

Convert the following in the polar form \(\frac { 1+3i }{ 1-2i } \)

Find the square root of -5+12i.

If a+ib =\(\frac { x+i }{ x-i } \) where x is real,prove that  a²+b²=1 and \(\frac { b }{ a } =\frac { 2x }{ { x }^{ 2 }-1 } \)