Use de Moivre's formula to evaluate (-2 + 2i)1º. Express your answer in standard form or, in a + bi form.

Q: Evaluate the expression (6 – 7i) + (3 – i) and write the result in the form a + bi. |- -

A:

Q: Find the 5™ roots of the complex number [(2+x) – 5i] , where x = last digit of your ID Number.

A: To find- Find the 5th roots of the complex number 2 + x - 5i, where x = 2

Q: Calculate (3 + i)*. Give your answer in a + bi form

A: Consider the complex number, Let,     z=3+i The polar form of the complex number z = a + ib is,…

Q: Evaluate the quotient, and write the result in the form a + bi.

A: To write the given expression in a+bi form: 5-i3+4i. Solution: 5-i3+4i On multiplying and dividing…

Q: Give the conjugate of 14i

A: Topic - complex number

Q: Express in the form , where a and b are a+bi real numbers.

A: 6-3i2+7i

Q: Express the product of 5iª(-7+ 9i8$) in a + bi form.

A:

Q: Express the product of 9i5(2i³ - 3i16) in a + bi form.

A: 9i15(2i3-3i16) =(9i15)(2i3)-(9i15)(3i16) =18i15+3 -27i(15+16) =18i18 - 27i31 Now i=√(-1) i18=-1…

Q: Express in the form , where a and b are a+bi real numbers.

A: We have to express given number 20-8i4i in the form a+bi where a and b are real numbers.

Q: Perform the indicated operations and express your answer in the form a + bi. √ (4 + 3i) (3i - 4)

A: Given expression is 4+3i3i-4. To perform the indicated operations and express answer in the form…

Q: Use DeMoivre’s theorem to find (–8)1/3. Express your answer in complex form.

A:

Q: Show that -1+ /3i is a cube root of 1 (meaning that its cube equals 1).

A: Find the cube of the expression and prove that it is equal to 1

Q: Evaluate the radical expression and express the result in the form a+bi. 2+v-8 1+v-2

A:

Q: Evaluate the product, and write the result in the form a + bi. (2 + 5i)(2 - 5i)

A: The given expression is (2 + 5i)(2 - 5i)

Q: Calculate (−1+i)5  . Give your answer in a+bi form.

A: Given,

Q: Express in a + bi form. 7+i 3 2i

A:

Q: What is the conjugate of - 3 + 4i?

A: Any number of the form a+ib where a and b are real numbers and i=-1 is called a complex number. The…

Q: Simplify the expression to a + bi form: (5 + 2i)(8 + 8i)

A: (5+2i)(8+8i) = 24 + 56i  The detailed solution is as follows below

Q: Show that the product of a+ bi and b+ai always results in a purely imaginary number, given that a…

A: Show that the product of (a+bi) and (b+ai) is a imaginary number . Here a and b are real number.

Q: Perform the indicated operations (answers in a + bi form): 3 + 4i / 3 – 4i

A:

Q: Perform the indicated operations and express your answer in the form a + bi. √ (3 + 4i) (4i - 3)

A: The given expression is 3+4i 4i-3. Simplify as follows.

Q: Simplify the expression to a + bi form: (4 – i)(2 – 3i)

A: Given: (4- i) (2-3i)

Q: Use de Moivre's Theorem to find the following. Write your answer in standard form. (−2√3+2i)4

A:

Q: Express the product (3 + 2i)(1 – 3i) in a + bi form.

A: Here we will use the product of two complex numbers

Q: Calculate (2 – i)°. Give your answer in a + bi form

A:

Q: Simplify the expression to a + bi form: (1+ 7i) + (4 – 10i) -

A: The given expression is 1+7i+4-10i.

Q: Evaluate the quotient, and write the result in the form a + bi.

A: Consider the provided expression, 4+6i3i Evaluate the quotient and write the result in the form a +…

Q: - 4i(10 – 7i)

A: -4i(10-7i)

Q: Evaluate the product, and write the result in the form a + bi. 4(-1 + 2i)

A: To evaluate the product: 4(-1+2i). Solution: 4(-1+2i) On simplifying further we get:…

Q: Express in the form , where a and b are a+bi real numbers.

A: To express the given expression in the form of (a+bi),where,(a,b∈R). (4+2i)(-5+4i) Solution:…

Q: Simplify and express in a + bi form: (12 + 3i) – (3 – i) 2.

A: 2. We need to simplify the following complex number expression 12+3i - 3-i

Q: Express in the form , where a and b are a+bi real numbers.

A: We have to express the express in a+bi form for the given expression: 3+8i2 We know that…

Q: Calculate (4 – i)'. Give your answer in a + bi form

A: The formula of the binomial theorem for the expansion of a+bn is given by a+bn=∑k=0nnkan-kbk.

Q: 6. Use DeMoivre's Theorem to calculate (–/3 + i) Write your answer in a + bi form.

A:

Q: The conjugate of 2 - 9i is________.

A: Given complex number z - z = 2-9i                       ....................(1)Concept - If a…

Q: calculate and write the quotient 4-i/3+2i in the a+bi form

A: Given,

Q: Find the quotient zi lza in standard form. 2= 3-3i, 22=1-i

A:

Q: Find all solutions of the equation and express them in the form a + bi.

A: Given: 70. t+3+3t=0

Q: Evaluate the product, and write the result in the form a + bi. (6 + 5i)( 2 - 3i)

A:

Q: Simplify and write in the form a+bi. (2+ 4i) + (–6 – 4i)

A: We have to simplify

Q: Evaluate and express in rectangular form: (1 + 2i) (4 - 6i^2) *

A:

Q: Simplify the expression to a + bi form: (-2+ 10i) + (–5 – 4i)

A: (-2 + 10i) + (-5 - 4i) = (-2-5) + (10i - 4i) = (-7) + (6i) = (-7) + (6)i  Where, a = - 7 & b = 6…

Q: Perform the indicated operation and write the result in standard form (a+bi) (3+2i)-(-5-6i)

A: Given  3+2i--5-6i

Q: Simplify the expression to a + bi form: (7+ 3i) – (-2 – 2i)

A: Here we find value of (7+3i)-(-2-2i)

Q: Express in the form , where a and b are a+bi real numbers.

A: Let the given expression be z - z = 7+5i--8+3iz = 7+5i+8-3iz = 7+8+5i-3iz = 15+2i

Q: c) By using De Moivre's theorem, find (3/5 – 3i) in the standard form.

A: To find complex no. in standard form using De Moivre's theorem .

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.