Complex Numbers · Mathematics · COMEDK

$$ \text { If }(1-4 i)^3=a+i b \text { then the value of } \mathrm{a} \text { and } \mathrm{b} \text { is } $$

$$ \text { The value of } \frac{i^{1004}+i^{1006}+i^{1008}+i^{1010}+i^{1012}}{i^{510}+i^{508}+i^{506}+i^{504}+i^{502}} \text { is } $$

$$ \text { The modulus of the following complex number } \frac{1+i}{1-i}-\frac{1-i}{1+i} \text { is } $$

If $$z=\sqrt{3}+i$$, then the argument of $$z^2 e^{z-i}$$ is equal to

If $$i=\sqrt{-1}$$ and $$n$$ is a positive integer, then $$i^n+i^{n+1}+i^{n+2}+i^{n+3}$$ is equal to

If $$\left(\frac{3}{2}+i \frac{\sqrt{3}}{2}\right)^{50}=3^{25}(x+i y)$$, where $$x$$ and $$y$$ are real, then the ordered pair $$(2 x, 2 y)$$ is

If the conjugate of $$(x+i y)(1-2 i)$$ be $$1+i$$, then

The argument of $${{1 - i\sqrt 3 } \over {1 + i\sqrt 3 }}$$ is

Evaluate $${\left[ {{i^{22}} + {{\left( {{1 \over i}} \right)}^{25}}} \right]^3}$$

$${(i + \sqrt 3 )^{100}} + {(i - \sqrt 3 )^{100}} + {2^{100}}$$ is equal to

What is the argument of the complex number $${{(1 + i)(2 + i)} \over {3 - i}}$$, where $$i = \sqrt { - 1} $$ ?

Evaluate $${\left[ {{i^{18}} + {{\left( {{1 \over i}} \right)}^{25}}} \right]^3}$$.

If $${(\sqrt 3 + i)^{100}} = {2^{99}}(a + ib)$$, then $${a^2} + {b^2}$$ is equal to

The conjugate of the complex number $${{{{(1 + i)}^2}} \over {1 - i}}$$ is

The imaginary part of $$i^i$$ is

The amplitude of $${(1 + i)^5}$$ is

If $$1,\omega ,{\omega ^2}$$ are the cube roots of unity, then $$(1 + \omega )(1 + {\omega ^2})(1 + {\omega ^4})(1 + {\omega ^8})$$ is equal to