if a ib c id e if g ih a ib then a 2 b 2 544030689

If $$\left( {a + ib} \right)\left( {c + id} \right)\left( {e + if} \right)\left( {g + ih} \right) = A + iB,$$ then $$\left( {{a^2} + {b^2}} \right)\left( {{c^2} + {d^2}} \right)\left( {{e^2} + {f^2}} \right)\left( {{g^2} + {h^2}} \right) = $$

A. $${A^2} + {B^2}$$

B. $${A^2} - {B^2}$$

C. $$A^2$$

D. $$B^2$$

Answer : $${A^2} + {B^2}$$

Solution :
$$\eqalign{ & \left( {a + ib} \right)\left( {c + id} \right)\left( {e + if} \right)\left( {g + ih} \right) = A + iB\,\,\,\,.....\left( {\text{i}} \right) \cr & \Rightarrow \,\left( {a - ib} \right)\left( {c - id} \right)\left( {e - if} \right)\left( {g - ih} \right) = A - iB\,\,\,.....\left( {{\text{ii}}} \right) \cr} $$
Multiplying (i) and (ii), we get
$$\left( {{a^2} + {b^2}} \right)\left( {{c^2} + {d^2}} \right)\left( {{e^2} + {f^2}} \right)\left( {{g^2} + {h^2}} \right) = {A^2} + {B^2}$$

Releted MCQ Question on
Algebra >> Complex Number

Releted Question 1

If the cube roots of unity are $$1,\omega ,{\omega ^2},$$ then the roots of the equation $${\left( {x - 1} \right)^3} + 8 = 0\,\,{\text{are}}$$

A. $$ - 1,1 + 2\omega ,1 + 2{\omega ^2}$$

B. $$ - 1,1 - 2\omega ,1 - 2{\omega ^2}$$

C. $$- 1, - 1, - 1$$

D. none of these

View Answer

Releted Question 2

The smallest positive integer $$n$$ for which $${\left( {\frac{{1 + i}}{{1 - i}}} \right)^n} = 1\,{\text{is}}$$

A. $$n = 8$$

B. $$n = 16$$

C. $$n = 12$$

D. none of these

View Answer

Releted Question 3

The complex numbers $$z = x+ iy$$ which satisfy the equation $$\left| {\frac{{z - 5i}}{{z + 5i}}} \right| = 1$$ lie on

A. the $$x$$ - axis

B. the straight line $$y = 5$$

C. a circle passing through the origin

D. none of these

View Answer

Releted Question 4

If $$z = {\left( {\frac{{\sqrt 3 }}{2} + \frac{i}{2}} \right)^5} + {\left( {\frac{{\sqrt 3 }}{2} - \frac{i}{2}} \right)^5},\,{\text{then}}$$

A. $${\text{Re}}\left( z \right) = 0$$

B. $${\text{Im}}\left( z \right) = 0$$

C. $${\text{Re}}\left( z \right) > 0,{\text{Im}}\left( z \right) > 0$$

D. $${\text{Re}}\left( z \right) > 0,{\text{Im}}\left( z \right) < 0$$

View Answer

If $$\left( {a + ib} \right)\left( {c + id} \right)\left( {e + if} \right)\left( {g + ih} \right) = A + iB,$$ then $$\left( {{a^2} + {b^2}} \right)\left( {{c^2} + {d^2}} \right)\left( {{e^2} + {f^2}} \right)\left( {{g^2} + {h^2}} \right) = $$

Releted MCQ Question on
Algebra >> Complex Number

If the cube roots of unity are $$1,\omega ,{\omega ^2},$$ then the roots of the equation $${\left( {x - 1} \right)^3} + 8 = 0\,\,{\text{are}}$$

The smallest positive integer $$n$$ for which $${\left( {\frac{{1 + i}}{{1 - i}}} \right)^n} = 1\,{\text{is}}$$

The complex numbers $$z = x+ iy$$ which satisfy the equation $$\left| {\frac{{z - 5i}}{{z + 5i}}} \right| = 1$$ lie on

If $$z = {\left( {\frac{{\sqrt 3 }}{2} + \frac{i}{2}} \right)^5} + {\left( {\frac{{\sqrt 3 }}{2} - \frac{i}{2}} \right)^5},\,{\text{then}}$$

Practice More Releted MCQ Question on
Complex Number

Practice More MCQ Question on Maths Section

If $$\left( {a + ib} \right)\left( {c + id} \right)\left( {e + if} \right)\left( {g + ih} \right) = A + iB,$$ then $$\left( {{a^2} + {b^2}} \right)\left( {{c^2} + {d^2}} \right)\left( {{e^2} + {f^2}} \right)\left( {{g^2} + {h^2}} \right) = $$

Releted MCQ Question on Algebra >> Complex Number

If the cube roots of unity are $$1,\omega ,{\omega ^2},$$ then the roots of the equation $${\left( {x - 1} \right)^3} + 8 = 0\,\,{\text{are}}$$

The smallest positive integer $$n$$ for which $${\left( {\frac{{1 + i}}{{1 - i}}} \right)^n} = 1\,{\text{is}}$$

The complex numbers $$z = x+ iy$$ which satisfy the equation $$\left| {\frac{{z - 5i}}{{z + 5i}}} \right| = 1$$ lie on

If $$z = {\left( {\frac{{\sqrt 3 }}{2} + \frac{i}{2}} \right)^5} + {\left( {\frac{{\sqrt 3 }}{2} - \frac{i}{2}} \right)^5},\,{\text{then}}$$

Practice More Releted MCQ Question on Complex Number

Practice More MCQ Question on Maths Section

Releted MCQ Question on
Algebra >> Complex Number

Practice More Releted MCQ Question on
Complex Number