5) Evaluate and write the result in the form a + bi. ə) (-) 2+i b) 2-3i

Q: Express in terms of i. V- 121 V- 121 %3D (Simplify your answer. Type your answer in the form a +…

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Q: (b) Show that i³i is real, even though i or 3i is not.

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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: Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the…

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Q: 5. Expressed in a + bi form, is equivalent to 3+1 1)- 2- 3)- i 4) 15- 5i -5i

A: Given : 53+i

Q: 10 2. Use De Moivre's theorem to determine 1 in the form a + ib. 2

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Q: Write in the form a -/+ bi

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

A: 19--4

Q: Use De Moivre's Theorem to evaluate [-6+ 2i]6

A: Any complex number z=x+iy can be represented as  z=r(cos θ+isin θ) , where r=x2+y2, θ=tan-1 yx.  De…

Q: (b) Show that i0 is real, even though i or 6i is not.

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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: Use De Moivre's theorem to simplify the expression. Write the answer in a + bi form. (5 + 1)6 O 64 -…

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Q: 1-Show that У +їх ave X + iy =/=1 where Complex numbers ? X+iy and

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Q: Rewrite the equation in Ax + By = C form. %3D Use integers for A, B, and C. 1 y=- 2

A: We can rewrite the given equation as below

Q: b) By using De Moivre theorem, calculate in the form of a + bi: 4. i) (VZ – iv2)* | ii) (1– i)6

A: Given (2-i2)4 &   (1-i)6

Q: If Z = 2 + 5i, write down the conjugate of Z. Multiply Z by its conjugate and write answer in the…

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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: 6. Show that (1) Cou(B1, g) = 0 (2) Cov(3o, B1) %3D

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Q: 6. Express in a + bi form: 2i(i + 3)

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Q: Perform the computations in the given question and express the results in standard form a+ bi.   (2…

A: Given: 2-3i-1+4i Simplify the expression: 2-3i-1+4i=2-1+4i-3i-1+4i=-2+8i+3i-12i2=-2+11i-12i2

Q: Perform the computations in the given question and express the results in standard form a+ bi.   (2…

A: Given: 2-i3 Simplify using the identity (a-b)3=a3-b3-3ab(a-b). 2-i3=23-i3-3(2)(i)(2-i)

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

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Q: Express in terms of i -294 -294 = (Simplify youlanswer. Type your answer in the form a + bi.)

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Q: -- Write z -5- iz + 3i in a + bi form

A: z in complex form is written as x + iy z¯ in complex form is written as x - iy Using these two…

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: Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the…

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Q: а. Complete the basis step of the proof.

A: To prove that:              ∑i=0n2i=2n+1-1  for any nonnegative integer n.

Q: Use DeMoivre's Theorem to expand  answer in a+bi form using exact values

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Q: What is the midpoint between z1 = 9i and z2 = 4? (2, 4.5) (-4,-9) (-2,-4.5) (4, 9)

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Q: State the conjugate of the following expressed in simplest a + bi form

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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: Use DeMoivre's Theorem to find the following. Write your answer in standard form. V2 cis- 20 O…

A: Given (√2cos(9π/20))5

Q: Perform the computations in the given question and express the results in standard form a+ bi.…

A: We have to perform the computations in the given question and express the results in standard form…

Q: 3. Express the product of 5i(-7+ 2it) in a + bi form.

A: Since, i2=-1 so i6=(i2)3=(-1)3=-1 i4=(i2)2=(-1)2=1

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

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Q: If z = 3 – 3i, express 5/z  in the form a + bi

A: The given value of z is z=3-3i.

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

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Q: Perform the computations in the given question and express the results in standard form a+ bi. 1/2-i

A: z=12-irationalise the denominator z=12-i×2+i2+iz=1(2+i)(2-i)(2+i)using the identity…

Q: (ii) A = 82 + &V1+ 4

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

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Q: 9. Express (3 – 2i)² in a + bi form.

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Q: Perform the computations in the given question and express the results in standard form a+ bi. (5 -…

A: The standard form is  a+biSo,(5−3i)(2−4i)=10−8i-6i+12i2

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

A: The general form of complex number is :-       a+ bi , where a is real and b is imaginary part.…

Q: Use z = a + bi to show that z + -z = 2a and z - -z = 2bi.

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Q: Use DeMoivre Theorme to expand answer into a+bi form

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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: Perform the computations in the given question and express the results in standard form a+ bi.…

A: The given complex expression is, 5+2i5-2i The objective is to write the expression in standard form…

Q: 19. Express in a + bi form: (5 – 6yi)(4 + 8i) – [(2 – 3yi) – 3(1+ 6i)]

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