# If (2 + i) (2 + 2i) (2 + 3i) ... (2 + ni) = x + iy, then 5.8.13 ... (4 + n2) = ______. - Mathematics

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads
Fill in the Blanks

If (2 + i) (2 + 2i) (2 + 3i) ... (2 + ni) = x + iy, then 5.8.13 ... (4 + n2) = ______.

Advertisement Remove all ads

#### Solution

If (2 + i) (2 + 2i) (2 + 3i) ... (2 + ni) = x + iy, then 5.8.13 ... (4 + n2) = ______.

Explanation:

Given that (2 + i) (2 + 2i) (2 + 3i) ... (2 + ni) = x + iy  .....(1)

⇒ (bar(2 + i)) (bar(2 + 2i)) (bar(2 + 3i)) ... (bar(2 + ni)) = (bar(x + iy)) = (x – iy)

i.e., (2 – i) (2 – 2i) (2 – 3i) ... (2 – ni) = x – iy   ......(2)

Multiplying (1) and (2)

We get 5.8.13 ... (4 + n2) = x2 + y2.

Concept: Algebraic Operations of Complex Numbers
Is there an error in this question or solution?

#### APPEARS IN

NCERT Mathematics Exemplar Class 11
Chapter 5 Complex Numbers and Quadratic Equations
Solved Examples | Q 16.(vii) | Page 84

#### Video TutorialsVIEW ALL [1]

Share
Notifications

View all notifications

Forgot password?