Algebra of Complex Numbers

Q.

The value of $\frac{2+3i}{4+5i}$ is

1. 

2. 

3. 3 + 81i

4. None of these

Q.

The value of (3 + 4i) (6 - 7i) is

1. 46+3i

2. 18-28i

3. 46-3i

4. 18+28i

Q.

The value of $\frac{1}{2-3i}+7+8i$ is

1. 

2. 

3. 

4. 

Q.

If $\frac{c+i}{c-i}$ = a+ib, where a, b, c are real, then $a^2+b^2$ =

1. -1

2. 1

3. 

4. 

Q.

$\frac{1+7i}{(2-i{)}^2}$=

1. 

2. 

3. 

4. None of these

Q.

If (1+i)(1+2i)(1+3i)......(1+ni) = a+ib, then 2.5.10.....(1+$n^2$) is equal to

1. 

2. 

3. 

4. 

Q.

$\frac{1-i}{1+i}$ is equal to

1. 

2. 

3. 

4. None of these

Q.

If x=-5+$\sqrt{-4}$, then the value of the expression $x^4$+9$x^3$+35$x^2$-x+4 is

1. 160

2. -160

3. 60

4. -60

Q.

The equation $\overline{b}$z+$\overline{z}$b where b is a non-zero complex constant and c is real, represents

1. A circle

2. A straight line

3. A parabola

4. None of these

Q.

For any two complex number $z_1$ and $z_2$ and any real numbers a and b;
$|(a{z}_1-b{z}_2){|}^2$ + $|(b{z}_1-a{z}_2){|}^2$ =

1. (+)()

2. (+)

3. (+)

4. None of these