हिंदी

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

Advertisements
Advertisements

प्रश्न

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

योग
Advertisements

उत्तर

Let θ be the principal value of amplitude of 1 – i.

Since tanθ = –1

⇒ tanθ = `tan(- pi/4)`

⇒ θ = `- pi/4`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 5: Complex Numbers and Quadratic Equations - Solved Examples [पृष्ठ ८८]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 11
अध्याय 5 Complex Numbers and Quadratic Equations
Solved Examples | Q 24 | पृष्ठ ८८

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

If α and β are different complex numbers with |β| = 1, then find `|(beta - alpha)/(1-baralphabeta)|`


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

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


Write the conjugates of the following complex number:

3 + i


Write the conjugates of the following complex number:

3 – i


Write the conjugates of the following complex number:

cosθ + i sinθ


Find the value of i49 + i68 + i89 + i110 


If x + iy = (a + ib)3, show that `x/"a" + y/"b"` = 4(a2 − b2)


Find the value of x and y which satisfy the following equation (x, y∈R).

If x + 2i + 15i6y = 7x + i3 (y + 4), find x + y


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:

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


Solve the following equation for x, y ∈ R:

(4 − 5i)x + (2 + 3i)y = 10 − 7i


Answer the following:

Evaluate: (1 − i + i2)−15 


Answer the following:

Find the value of x3 + 2x2 − 3x + 21, if x = 1 + 2i


Answer the following:

Find the real numbers x and y such that `x/(1 + 2"i") + y/(3 + 2"i") = (5 + 6"i")/(-1 + 8"i")`


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


Find the value of 2x4 + 5x3 + 7x2 – x + 41, when x = `-2 - sqrt(3)"i"`.


State true or false for the following:

If three complex numbers z1, z2 and z3 are in A.P., then they lie on a circle in the complex plane.


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 value of `(i^(4n + 1) -i^(4n - 1))/2`?


The area of the triangle on the complex plane formed by the complex numbers z, –iz and z + iz is ______.


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 value of `sqrt(-25) xx sqrt(-9)` is ______.


The number `(1 - i)^3/(1 - i^2)` is equal to ______.


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


Which of the following is correct for any two complex numbers z1 and z2?


The point represented by the complex number 2 – i is rotated about origin through an angle `pi/2` in the clockwise direction, the new position of point is ______.


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


If α, β, γ and a, b, c are complex numbers such that `α/a +  β/b + γ/c` = 1 + i and `a/α +  b/β + c/γ` = 0, then the value of `α^2/a^2 +  β^2/b^2 + γ^2/c^2` is equal to ______.


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

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


Find the value of `(i^592+i^590+i^588+i^586+i^584)/(i^582+i^580+i^578+i^576+i^574)`


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

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


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

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


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)`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×