The smallest positive integer "k" for which $(\frac{1+i}{1-i})^k=1$ is;

$(\frac{1-i}{1+i})^{100}=x+iy$ then:

For De Moivre's Theorem, $n$ belongs to which of the following sets?

If $Z_{1}=3-6i \, , Z_{2}=4+5i$ the $Z_{1}Z_{2}=?$

Find the real part in $(\cos{\theta}-i\sin{\theta})^2$, for $\theta=45^o$

If $Z=a+b$ then $|Z|=?$

If $a>b$, then $ax>bx$, when $x$

$(\frac{1}{2}+\frac{i\sqrt{3}}{2})^6=?$

Conjugate of $(-3, 4)$ is

If $Z=(a,b)$ then multiplicative inverse of $Z$ is

$\mathbb{C}$ has no identity with respect to $+$ other than _____.

$|x^2|$=?

The value of $i^{-29}$ is

The value of $(3+2i)^3$ is

The multiplicative inverse of $\sqrt{7}$ is ________

The value of $i^{25}=?$

The absolute value of $z=\frac{1+i}{3-i}$ is:

$i^{15}=?$

Find the imaginary part of $(2+3i)^3$=?

If $'a'$ and $'b'$ are real numbers then $a+b$ is a real no. This law is called

Additive inverse of $2+\sqrt{3}$ is ______

Which of the following is field?

If $Z=x+iy$, then $Z^2=|Z|^2$ if

Find $(\overline{z})^2$ if $z=2\sqrt{3}i$

Associative property of Multiplication is applicable on:

$0.\overline{3575}$ is_______

Set of even prime natural numbers is;

If $\cos{\theta}+i\sin{\theta}$, then $\frac{1}{Z}$=?

If $Z\, \in\, \mathbb{C}$ the $\overline{Z_1+Z_2}=?$

If $Z_{1}=(x_{1} , y_{1}) \, , Z_{2}=(x_{2} , y_{2})$ where $Z_{1}\, ,\, Z{2}\,\in\,\mathbb{C}$ then $Z_{1}+Z_{2}=?$

Real part of $(2-3i)^6$ is;

$(3,5)+(0,4)=?$

$i$ expressed in the form of coordinates is;

$|\frac{1+i}{1+\frac{1}{i}}|=?$

The $\{x\,\in\,R, x^2+10=0\}$ is______

If $(\cos{\theta}+i\sin{\theta})^2=x-iy$ then $x^2+y^2=?$

The modulus of the complex number $1+i\tan{\alpha}$=?

$1>-1\,\Rightarrow\,-3>-5$, this property is called

Find the multiplicative inverse of complex number $z=5+i$

If $Z=\frac{2+7i}{2-8i}$, then $Z=\frac{2-7i}{2+8i}$=?

Additive identity of complex numbers

If $a>b$, then according to addition properties of inequalities $a+c$ ______ $c+b$

If $a$ and $b$ are two non negative numbers such that $a>b$, then: $\frac{\frac{1}{a}-\frac{1}{b}}{\frac{1}{a}+\frac{1}{b}}$ is:

The conjugate of $\frac{2+3i}{-i+1}=?$

Modulus of $i$ is equal to:

If $Z$ is a complex number then the minimum value of $|Z|+|Z-1|$ is _________

In $n$ is any positive integer then the value of $\frac{i^{4n+1}-i^{4n-1}}{2}=?$

Which one of the following is the real part of the complex number: $6(2-3i)$?

Multiplicative inverse of a non-zero element $a\,\in\,Z$ is ____

Real Component of $(4-i)^2$ is:

Additive inverse of a complex number $(a, b)$ is written as:

$(-1+\sqrt{-3})^4+(-1-\sqrt{-3})^4=?$

Let $a,b,c,d\,\in\,\mathbb{R}$ then $a=b$ and $c=d$ $\Rightarrow$

$(-i)^{31}$

If $\frac{Z_1}{Z_2}$ is purely imaginary then $|\frac{Z_1+Z_2}{Z_1-Z_2}|$=?

If Z=$a+b$, then $\overline{Z}=?$

If $Z=4+6i^2$ then $|Z| =?$

Additive inverse of $(3,3)$ in $\mathbb{C}$ is

The polar coordinates of a point are $(2, 319)$ then the Cartesian coordinates

If $a\,\in\,\mathbb{R}$ then multiplicative inverse of $a$ is

The multiplicative inverse of $1-3i$ is

The set of rational numbers between two real numbers is _______

$\{1, -1\}$ is closed with respect to;

What is the area of a rectangular room with length of $5-3i$ and width of $2i$?

$Arg(\frac{Z_1}{Z_2})=?$

If $\frac{a}{b}=\frac{c}{d}$ then $\frac{a+b}{a-b}=\frac{c+d}{c-d}$ represents __________ Property.

If $Z_{1}=(1,0) \, , Z_{2}=(2,3)$ the $Z_{1}Z_{2}=?$

$\frac{\sqrt{18}}{\sqrt{72}}$ is;

$2\sqrt{-9}\, \times\, \sqrt{-16}=?$