English

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

Advertisements
Advertisements

Question

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

Sum

Solution

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

Since tanθ = –1

⇒ tanθ = `tan(- pi/4)`

⇒ θ = `- pi/4`

shaalaa.com
  Is there an error in this question or solution?
Chapter 5: Complex Numbers and Quadratic Equations - Solved Examples [Page 88]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 11
Chapter 5 Complex Numbers and Quadratic Equations
Solved Examples | Q 24 | Page 88

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Find the multiplicative inverse of the complex number.

`sqrt5 + 3i`


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


If (a + ib) (c + id) (e + if) (g + ih) = A + iB, then show that (a2 + b2) (c2 + d2) (e2 + f2) (g2 + h2) = A2 + B2.


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


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

(2 + 3i)(1 – 4i)


Write the conjugates of the following complex number:

cosθ + i sinθ


Select the correct answer from the given alternatives:

If n is an odd positive integer then the value of 1 + (i)2n + (i)4n + (i)6n is :


Answer the following:

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

`3 + sqrt(-64)`


Answer the following:

Show that `(1/sqrt(2) + "i"/sqrt(2))^10 + (1/sqrt(2) - "i"/sqrt(2))^10` = 0


Answer the following:

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


Answer the following:

Show that z = `((-1 + sqrt(-3))/2)^3` is a rational number


If z1 = 5 + 3i and z2 = 2 - 4i, then z1 + z2 = ______.


If z1 = 2 – 4i and z2 = 1 + 2i, then `bar"z"_1 + bar"z"_2` = ______.


Locate the points for which 3 < |z| < 4.


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


State true or false for the following:

The points representing the complex number z for which |z + 1| < |z − 1| lies in the interior of a circle.


If |z + 1| = z + 2(1 + i), then find z.


State True or False for the following:

Multiplication of a non-zero complex number by –i rotates the point about origin through a right angle in the anti-clockwise direction.


State True or False for the following:

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


If z is a complex number, then ______.


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 ______.


If `(x + iy)^(1/5)` = a + ib, and u = `x/a - y/b`, then ______.


A complex number z is moving on `arg((z - 1)/(z + 1)) = π/2`. If the probability that `arg((z^3 -1)/(z^3 + 1)) = π/2` is `m/n`, where m, n ∈ prime, then (m + n) is equal to ______.


The smallest positive integer n for which `((1 + i)/(1 - i))^n` = –1 is ______.


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 ______.


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.

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


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 `sqrt(-3) xx sqrt(-6)`


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

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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×