In Exercises 1–4, write the complex number instandard form.1. 6 + √−4 2. 3 − √−253. i2 + 3i 4. −5i + i2

Q: Solve, z2 - 4z + 5 = 0 Given that z, = 3 + i, z2 = 4 – 3i, z3 = -1+ 2i and z4 = -2 – 5i, determine…

A: Given equation is, z2-4z+5=0 Now, z=4±16-4×52⇒z=4±-42⇒z=4±2i2=2±i So, the solutions are z=2+i, 2-i

Q: In Exercises 23–25, solve each equation. If the solution set is Ø or (-0, ), classify the equation…

A: 23). Given equation is 32x-4=9-3x+1. To solve the given equation. Solution: Solving the given…

Q: Write the given numbers in the form a + bi where a, bER (1) (–2+2i)³ (5-4i) - (3+7i) (ii) 4+2i) + (2…

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Q: For Exercises 23–30, convert the complex number from polar form to rectangular form a + bi. (See…

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Q: In Exercises 9–12, find all real solutions to the equations.

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Q: 2. Write the number (2 – i)(-1+3i)(3 – 4i) in the form of +bi .

A: The detailed solution is as follows below:

Q: Find a - b

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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: For Exercises 31–56, perform the indicated operations. Write the answers in standard form, a + bi.…

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

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

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Q: (8a in simplest form.

A: 8a-3-23To write in simplest form

Q: Exercises 38–40 will help you prepare for the material covered in the first section of the next…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

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: Simplify the complex power [(1+i)/(1-i)]-2i  and leave your answer in its simplest form.

A: Use the following formulae, to obtain the solution.…

Q: 6. Write the complex number is standard form (a + bi) 14- V-98 -7

A: As we know from the radical rule: -a=-1a   Given: 14--98-7

Q: For Exercises 19–26, simplify each expression and write the result in standard form, a + bi. 8 + 3i…

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Q: For Exercises 99–103, perform the indicated operations. 1 + =i 6. 99. + -i 100. (4 – 7i)(5 + i) 3 5…

A: 99. Given expression, 23+35i-16+25i Now simplify the given expression, 23+35i-16+25i=23-16+35-25i…

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

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Q: 14. Which eguation demonstrates the commutative property of addition for complex numbers? (10 – 5i)…

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Q: In Exercises 20–21, solve each rational equation. 11 20. x + 4 + 2 x2 – 16 - x + 1 21. x? + 2x – 3 1…

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Q: 2. Write the given complex numbers in the form a + bi. 3 (a) 를 + 을-2유 (b) 2,0 + + 5i 5- 12i (c) 2-4i…

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Q: 3. (Complex Numbers: Quadratic Equations; Scientific Calculators). Solve the quadratic equation 2² +…

A: The given complex equation is z2+(6-3i)z+15-23i=0. (i) To find: Discriminant of the above equation.…

Q: Simplify the complex number 7 (²+1) ³ - 5 (¹)² and express it in the standard form.

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Q: For Exercises 5–10, a. Simplify the expression. b. Substitute 0 for h in the simplified expression.…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…