Advertisements
Advertisements
Question
Evaluate: (1 + i)6 + (1 – i)3
Solution
(1 + i)6 = {(1 + i)2}3
= (1 + i2 + 2i)3
= (1 – 1 + 2i)3
= 8i3
= –8i
And (1 – i)3 = 1 – i3 – 3i + 3i2
= 1 + i – 3i – 3
= –2 – 2i
Therefore, (1 + i)6 + (1 – i)3
= –8i – 2 – 2i
= –2 – 10i
APPEARS IN
RELATED QUESTIONS
Express the following expression in the form of a + ib.
`((3 + sqrt5)(3 - isqrt5))/((sqrt3 + sqrt2i)-(sqrt3 - isqrt2))`
Simplify the following and express in the form a + ib:
`(sqrt(5) + sqrt(3)"i")/(sqrt(5) - sqrt(3)"i")`
Find the value of : x3 + 2x2 – 3x + 21, if x = 1 + 2i
Write the conjugates of the following complex number:
`sqrt(2) + sqrt(3)"i"`
Is (1 + i14 + i18 + i22) a real number? Justify your answer
Select the correct answer from the given alternatives:
`sqrt(-3) sqrt(-6)` is equal to
Answer the following:
Solve the following equation for x, y ∈ R:
`(x + "i"y)/(2 + 3"i")` = 7 – i
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:
Show that `(1/sqrt(2) + "i"/sqrt(2))^10 + (1/sqrt(2) - "i"/sqrt(2))^10` = 0
Answer the following:
show that `((1 + "i")/sqrt(2))^8 + ((1 - "i")/sqrt(2))^8` = 2
Answer the following:
If x + iy = `("a" + "ib")/("a" - "ib")`, prove that x2 + y2 = 1
Answer the following:
Simplify: `("i"^65 + 1/"i"^145)`
If z1 = 5 + 3i and z2 = 2 - 4i, then z1 + z2 = ______.
Find the value of 2x4 + 5x3 + 7x2 – x + 41, when x = `-2 - sqrt(3)"i"`.
The real value of ‘a’ for which 3i3 – 2ai2 + (1 – a)i + 5 is real is ______.
If (2 + i) (2 + 2i) (2 + 3i) ... (2 + ni) = x + iy, then 5.8.13 ... (4 + n2) = ______.
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.
What is the reciprocal of `3 + sqrt(7)i`.
The equation |z + 1 – i| = |z – 1 + i| represents a ______.
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.
A real value of x satisfies the equation `((3 - 4ix)/(3 + 4ix))` = α − iβ (α, β ∈ R) if α2 + β2 = ______.
Let x, y ∈ R, then x + iy is a non-real complex number if ______.
If z1, z2, z3 are complex numbers such that |z1| = |z2| = |z3| = `|1/z_1 + 1/z_2 + 1/z_3|` = 1, then |z1 + z2 + z3| is ______.
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)`
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)`
