# If (1+I)(1 + 2i)(1+3i)..... (1+ Ni) = A+Ib,Then 2 ×5 ×10 ×...... ×(1+N2) is Equal To. - Mathematics

MCQ

If (1+i)(1 + 2i)(1+3i)..... (1+ ni) = a+ib,then 2 ×5 ×10 ×...... ×(1+n2) is equal to.

#### Options

• sqrt(a^2 +b^2)

• sqrt(a^2 +b^2)

• sqrt(a^2 - b^2)

• a^2 +b^2

• a^2 -b^2

• a+b

#### Solution

a^2 +b^2

(1 + i)(1 + 2i)(1 + 3i) ......(1 + ni) = a + ib

Taking modulus on both the sides, we get:

|(1+i)(1+2i) (1+3i).............. (1+ni)| = |a+ib|

|(1+i)(1+2i)(1+3i)..............(1+ni)|can be written as |(1+i)|  |(1+2i)|  |(1+3i)|........|(1+ ni)|

$\sqrt{1^2 + 1^2} \times \sqrt{1^2 + 2^2} \times \sqrt{1^2 + 3^2} \times . . . \times \sqrt{1 + n^2} = \sqrt{a^2 + b^2}$

$\Rightarrow \sqrt{2} \times \sqrt{5} \times \sqrt{10} \times . . . \times \sqrt{1 + n^2} = \sqrt{a^2 + b^2}$

Squaring on both the sides, we get:

$2 \times 5 \times 10 \times . . . \times (1 + n^2 ) = a^2 + b^2$

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 13 Complex Numbers
Q 3 | Page 63