Home
Class 12
MATHS
Show that ((19- 7i)/(9 + i))^(12) + ((...

Show that
`((19- 7i)/(9 + i))^(12) + ((20 - 5i)/(7 - 6i))^(12)` is real.

Text Solution

Verified by Experts

The correct Answer is:
`z` is purely real.
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    PREMIERS PUBLISHERS|Exercise Solution to Exercise 2.5|15 Videos
  • COMPLEX NUMBERS

    PREMIERS PUBLISHERS|Exercise Solution to Exercise 2.6|11 Videos
  • COMPLEX NUMBERS

    PREMIERS PUBLISHERS|Exercise Solution to Exercise 2.3|5 Videos
  • APPLICATIONS OF VECTOR ALGEBRA

    PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE (Answer the following questions)|21 Videos
  • DIFFERENTIALS AND PARTIAL DERIVATIVES

    PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE|40 Videos

Similar Questions

Explore conceptually related problems

Show that ((19 + 9i)/(5 - 3i))^(15) - ((8 + i)/(1 + 2i))^(15) is purely imaginary

Show that ((19+9i)/(5-3i))^(15)-((8+i)/(1+2i))^(15) is purely imaginary.

If n_1, n_2 are positive integers, then (1 + i)^(n_1) + ( 1 + i^3)^(n_1) + (1 + i_5)^(n_2) + (1 + i^7)^(n_2) is real if and only if :

|(1+7i)/(4+3i)|=

If x + iy = (3 + 5i)/(7-6i), they y =

Conver the following in the polar form: (i) (1+7i)/(2-i)^(2) , (ii) (1+3i)/(1-2i)

Simplify the following : (i) i^7 " " (ii) i^(1729) " " (iii) i^(-1924) + i^(2018) " " (iv) sum_(n=1)^(102) i^(n) " " (v) i i^2 i^3 …..i^(40)