Advertisements
Advertisements
Question
Let x, y ∈ R, then x + iy is a non-real complex number if ______.
Options
x = 0
y = 0
x ≠ 0
y ≠ 0
Advertisements
Solution
Let x, y ∈ R, then x + iy is a non-real complex number if y ≠ 0.
Explanation:
x + yi is a non-real complex number if y ≠ 0.
If x, y ∈ R.
APPEARS IN
RELATED QUESTIONS
If α and β are different complex numbers with |β| = 1, then find `|(beta - alpha)/(1-baralphabeta)|`
If `((1+i)/(1-i))^m` = 1, then find the least positive integral value of m.
Find the value of i49 + i68 + i89 + i110
Find the value of: x3 – x2 + x + 46, if x = 2 + 3i
Find the value of: 2x3 – 11x2 + 44x + 27, if x = `25/(3 - 4"i")`
Simplify the following and express in the form a + ib:
`(5 + 7"i")/(4 + 3"i") + (5 + 7"i")/(4 - 3"i")`
Find the value of: x3 – 5x2 + 4x + 8, if x = `10/(3 - "i")`.
Simplify:
`(i^592 + i^590 + i^588 + i^586 + i^584)/(i^582 + i^580 + i^578 + i^576 + i^574)`
Find the value of 1 + i2 + i4 + i6 + i8 + ... + i20
Show that 1 + i10 + i100 − i1000 = 0
If (x + iy)3 = y + vi then show that `(y/x + "v"/y)` = 4(x2 – y2)
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:
`(sqrt(5) + sqrt(3)"i")/(sqrt(5) - sqrt(3)"i")`
Answer the following:
Solve the following equations for x, y ∈ R:
(x + iy) (5 + 6i) = 2 + 3i
Show that `(1/sqrt(2) + "i"/sqrt(2))^10 + (1/sqrt(2) - "i"/sqrt(2))^10` = 0
Answer the following:
Simplify: `("i"^65 + 1/"i"^145)`
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 complex number cosθ + isinθ can be zero for some θ.
1 + i2 + i4 + i6 + ... + i2n is ______.
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:
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:
The inequality |z – 4| < |z – 2| represents the region given by x > 3.
Where does z lie, if `|(z - 5i)/(z + 5i)|` = 1.
The real value of α for which the expression `(1 - i sin alpha)/(1 + 2i sin alpha)` is purely real 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 ______.
`((1 + cosθ + isinθ)/(1 + cosθ - isinθ))^n` = ______.
If a complex number z satisfies the equation `z + sqrt(2)|z + 1| + i` = 0, then |z| is equal to ______.
The complex number z = x + iy which satisfy the equation `|(z - 5i)/(z + 5i)|` = 1, lie on ______.
If `|(6i, -3i, 1),(4, 3i, -1),(20, 3, i)|` = x + iy, then ______.
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.
`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18)`
i2 + i3 + ... + i4000 =
