Rewrite each of the following expressions involving complex numbers in the form a+ bi where a and b are real numbers. a. (3+ 21)(2 – Si) b. (5 + 4)(17 – 136) -(5+ 36)(17 – 136) d. (1 + )(13 – 4i)(1 - i) e. I+i+f +?

Q: Express the following in the form a + bi, where a and b are real numbers: 3-4i

A: Explanation; Given that: Concept: Make a perfect square.

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: Reduce the quality 5i to (1-i)(2-i)(3-i) real number.

A: Now we reduce the quality  5i(1-i)(2-i)(3-i) to real number.   5i(1-i)(2-i)(3-i)…

Q: 7) What are the real and imaginary parts of (1+3i)exp(-ir/4)/(6+8i)?

A: The given complex number,        1+3iexp-iπ4/6+8i

Q: Let z be any complex number and let Im2| <|2], then which one of the following inequalities is true?…

A: We have to solve given problem:

Q: 6. Evaluate the following and leave your answer in standard form [(1 – 4i)-1 – 2(i + 1)-'[(3 – 4i)(i…

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Q: 1 was placed in the form ax where a and b are real numbers, then which of the 2x 3. If the…

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Q: Which of the following is not a real number? (1) (6 + 2i)(6 – 2i) (2) (–2i)12 (3) (3 + 4i)(-4i) (4)…

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

A: 6-3i2+7i

Q: (-3-15)(-1.23+/2.1)

A: The given problem is to find the principal value of the given complex number. Given complex number…

Q: 1. Simplify the complex mumbers below. i (3+ 5) + (10-14) i. (3+5) - (10 -14) i. (3+ 5)(10-14i)

A: According to the given information it is required to simplify the complex numbers given in each…

Q: Which of the following is the standard form for the product of (2 + 3i)(2 3i)?

A:

Q: Express 3-i/2+3i  in the form a + bi

A: Rationalise i^2=-1

Q: ii) How would you describe geometrically the relationship between a nonzero complex number z = a +…

A: Given: Describe geometrically the relationship between z=a+ib anda. −zb. z−1

Q: The Complex number z is defined as 2- il1+i](1-2;) gven tnt (2-3i)+ p(z-3)=7FE where Paud 7 are real…

A: The complex number z is defined as z=i1+i1-2i2

Q: 4. What is the simplification of the following complex expression (i? = -1) 5-i 3+i %3D a) 7/5 -…

A: Given the complex expression=5−i3+i

Q: 11. Write the quotient of the complex numbers in the standard form z=x+ iy. 3+i 1-2i

A: If you like the solution then please give it a thumbs up.... The Answer is:           Standard form…

Q: Express the following in the form a + bi, where a and b are real numbers: 60i-11

A: Introduction: Like a real number, the square roots of a complex number can also be determined. A…

Q: Write the following as a complex number in the form a+bi x4-8x2-48=0

A: To write the following as a complex number in the form a+bi x4-8x2-48=0

Q: Find the real numbers x and y if (x – iy) (3 + 5i) is the conjugate of –6 – 24i.

A:

Q: 4. Perform the following operations involving complex numbers: a. (2 + 7i) + (3 – 4i) b. (9 + 5i) -…

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Q: Evaluate the following complex numbers: (a) [(5 + j2)(-1+ j4) – 5/60°]* 10 + j5+3/40° -3+ j4 (b) +…

A: (a).  The given polar equation is: 5+j2-1+j4-5∠60°

Q: What is the sum of 2 + 3i and -1 + 7i? A 1+ 10i 3 – 4i

A: here we want to add 2+ 3i and -1 + 7i

Q: Find the argument of the complex number 3 + 17i - 9. 9T - 4 97 4

A: To find the argument of given complex number

Q: Express the following complex number in exponential form: (3 - 4) O -V5e-5.36/ 5e5.361 5e-5.36i…

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Q: what Is the gimplest form of 5i (1-i) (2-i) (3-i) a. -10i -5/3 C. b. -8i d. -V½

A:

Q: Reduce each of these quantities to a real number: (a) 1 + 2i + 3 - 4i 2-i 5i (b) 5i (1 - i)(2 - i)…

A: (a) Here given the complex number 1+2i3-4i+2-i5i to reduce this complex number first take the HCF of…

Q: Perform the following operations on the complex numbers. a) (4– 6i) – (-8 - 9i) b) (4 – 6i)(-8 – 9i)…

A: (a) Perform the subtraction operation for the given complex numbers.…

Q: 1. Simplify the following list of complex expressions to the form a + ib where a, b are real…

A: we need to simplify the given complex expression to the form a+ib we know i=-1,  i2 = -1,  i3=-i, i4…

Q: What is the simplified complex expression of (4.33 +2.5i)??

A: Solution :  Given that (4.33 + 2.5i)2

Q: Express the following in a + ib form a. (4i-7)+(2+i) b. (5-2i)(2+ 2i)

A:

Q: (b) Show that it is real, even though i or 8i is not.

A:

Q: 4Q Express 2= (1+2i)² 7-i in the form a + ib where a and b are real numbers.

A:

Q: Rewrite each of the following expressions involving complex numbers in the form a+ bi where a and b…

A: (a)(3+2i)2-5i =32-35i+2i2-2i5i3+2i2-5i = 6-15i+4i-10i23+2i2-5i = 6-11i-10-1…

Q: Express the result of each of these complex numbers manipulations in polar form.

A:

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 the following complex number in exponential form: (-1 – 5) 3.1 e2.5i 5.1 e4.5i -5.1 e4.5i…

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Q: Find the modulus, Izl, and argument, 8, of the complex number. -1+i One charaes 4.6

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Q: Express (5 – 3i)3 in the form a + ib.

A:

Q: 10. Write 2e' the complex form of a + bi.

A: Given exponential form, 2eπ3i

Q: 15. Match each expression on the left to its complex form a + bi on the right. 1. -V-64+8 а. —3 + 3і…

A: We have to match expressions to their complex form.

Q: 2. Write each complex number in polar form with an argument 0 between 0 and 2n. Do not multiply it…

A: Explained below...

Q: Write the following complex numbers in the form a+ib: 5 e7 1/4 = + i 2 el7 x/6 + i 7 e'5 z/3 + i 4…

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Q: (b) Show that ii is real, even though i or 5i is not.

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Q: Match each definition to the corresponding term. 1. the set of all numbers written in the form a.…

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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: 4. Simplify. Write each expression in the form a + bi: a. (5 – 21) + (-3 +7i) b. (5 – 2i) – (-3 +…

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Q: b, be complex numbers and N a positive natural number such N¬I i2knx N = απ Τ n = 0 to N - 1 k=0

A:

Q: Consider the following definitions of imaginary numbers: x=4−2i y=6+7i z=5i Then, x+y−2z=?

A: We plug the given values in the expression x+y-2z