मराठी

If a + ib = c + id, then ______.

Advertisements
Advertisements

प्रश्न

If a + ib = c + id, then ______.

पर्याय

  • a2 + c2 = 0

  • b2 + c2 = 0

  • b2 + d2 = 0

  • a2 + b2 = c2 + d2

MCQ
रिकाम्या जागा भरा
Advertisements

उत्तर

If a + ib = c + id, then a2 + b2 = c2 + d2.

Explanation:

Given that: a + ib = c + id

⇒ |a + ib| = |c + id|

⇒ `sqrt(a^2 + b^2) = sqrt(c^2 + d^2)`

Squaring both sides, we get

a2 + b2 = c2 + d2 

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Complex Numbers and Quadratic Equations - Exercise [पृष्ठ ९६]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 11
पाठ 5 Complex Numbers and Quadratic Equations
Exercise | Q 44 | पृष्ठ ९६

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Express the following expression in the form of a + ib.

`((3 + sqrt5)(3 - isqrt5))/((sqrt3 + sqrt2i)-(sqrt3 - isqrt2))`


Reduce `(1/(1-4i) - 2/(1+i))((3-4i)/(5+i))` to the standard form.


Find the value of: x3 –  x2 + x + 46, if x = 2 + 3i


Simplify the following and express in the form a + ib: 

(2i3)2 


Simplify the following and express in the form a + ib:

(2 + 3i)(1 – 4i)


Simplify the following and express in the form a + ib:

`(4 + 3"i")/(1 - "i")`


Write the conjugates of the following complex number:

`-sqrt(5) - sqrt(7)"i"`


Write the conjugates of the following complex number:

5i


If a = `(-1 + sqrt(3)"i")/2`, b = `(-1 - sqrt(3)"i")/2` then show that a2 = b and b2 = a


Select the correct answer from the given alternatives:

The value of is `("i"^592 + "i"^590 + "i"^588 + "i"^586 + "i"^584)/("i"^582 + "i"^580 + "i"^578 + "i"^576 + "i"^574)` is equal to:


Answer the following:

Simplify the following and express in the form a + ib:

`3 + sqrt(-64)`


Answer the following:

Simplify the following and express in the form a + ib:

(1 + 3i)2(3 + i)


Answer the following:

Simplify the following and express in the form a + ib:

`(3"i"^5 + 2"i"^7 + "i"^9)/("i"^6 + 2"i"^8 + 3"i"^18)`


Answer the following:

Evaluate: (1 − i + i2)−15 


Answer the following:

Evaluate: i131 + i49 


Answer the following:

If x + iy = `("a" + "ib")/("a" - "ib")`, prove that x2 + y2 = 1


Answer the following:

Simplify: `("i"^238 + "i"^236 + "i"^234 + "i"^232 + "i"^230)/("i"^228 + "i"^226 + "i"^224 + "i"^222 + "i"^220)`


If |z1| = 1, |z2| = 2, |z3| = 3 and |9z1z2 + 4z1z3 + z2z3| = 12, then the value of |z1 + z2 + z3| is


The argument of the complex number `(4 + 9i)/(13 + 5i)` is ______


State true or false for the following:

If n is a positive integer, then the value of in + (i)n+1 + (i)n+2 + (i)n+3 is 0.


What is the principal value of amplitude of 1 – i?


For a positive integer n, find the value of `(1 - i)^n (1 - 1/i)^"n"`


If |z1| = |z2| = ... = |zn| = 1, then show that |z1 + z2 + z3 + ... + zn| = `|1/z_1 + 1/z_2 + 1/z_3 + ... + 1/z_n|`.


The sum of the series i + i2 + i3 + ... upto 1000 terms is ______.


State True or False for the following:

For any complex number z the minimum value of |z| + |z – 1| is 1.


State True or False for the following:

The inequality |z – 4| < |z – 2| represents the region given by x > 3.


The complex number z which satisfies the condition `|(i + z)/(i - z)|` = 1 lies on ______.


If the least and the largest real values of α, for which the equation z + α|z – 1| + 2i = 0 `("z" ∈ "C" and "i" = sqrt(-1))` has a solution, are p and q respectively; then 4(p2 + q2) is equal to ______.


Let z be a complex number such that `|(z - i)/(z + 2i)|` = 1 and |z| = `5/2`. Then the value of |z + 3i| is ______.


Show that `(-1 + sqrt3 i)^3` is a real number.


Simplify the following and express in the form a + ib.

`(3i^5 + 2i^7 + i^9) / (i^6 + 2i^8 + 3i^18)`


If z = 2 + i, then (z − 1) `(barz − 5) + (barz − 1)` (z − 5) is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×