Express the following in the form a + ib (for real a and b): 1 (a) 6+2i (b) (-+ i)¹ (c) i², i³, i4, i5,...

Q: b) Rationalize the numerator of 1 1 √7(x+h) √Tx - h Simplify your answer to the form A = A " where

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Q: Patricia derived the following incorrect formula by misapplying the Product Rule: a?y²) = x²(2y) +…

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Q: Add / subtract: A) (-1+ 2i) + (-2 + 5i) B) (2-3i) - (-2+ 3i)

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Q: S ((V80 – x2 ) – (0.3cos (1.2r + 1.3) + 5) d -(0.3cos(1.2x + 1.3) + 5) )dx

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Q: What does Sn represent in the following formula: Sn:a(r^n-1)/r-1 Give 2 reasons why r ≠ 1.

A: In the given question Sn represents that

Q: Given w (u) = 13 + 6u² and g(u) Enter the expression in simplest form. (wg)(u) = = 6u - 13, find…

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Q: 2. Simplify the following: 2 (m²)? ii) (62n* 1 ) ( 9 2n) (35+1 ) (2 2) i) ii) (2m³) 2 (3m) 2

A: Topic:- simplification

Q: 1 2 Perform the indicated operations when A = 0 -1 A(I + A) = =

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Q: Write the following numbers in a + bi form: () (а) —3 + i, (b) (-2 + 5i) – (1+ 5i) i, (c) + i, +

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Q: Suppose Zı= 4+4i , Z2= 5 +7i. Evaluate (a) 2 Z1– 4 Z2 Z2 (b) 3 Z1

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Q: Q28- The value of e-(In+1 )n is a) (-1)" e--1 b) (-1)"e" c) (-1)" e-+1 d) (-1)" e-"

A: We have to find value of  e-(in+1)π

Q: Perform this subtraction: (- 25 9x? – 5x) - ( 9a + x? + 8) |

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Q: (B) Evaluate f tan (7x +1) sec³(7x+1) dx.

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Q: Perform the indicated operations and simplify x2-16 x-4 a) x+3 5x2-45

A: Given : x2 - 16x + 3 ÷ x - 45x2 - 45

Q: Divide and express the result in standard form: (5 + 4i) / (4 - i).

A: Given:5+4i4-i

Q: Write (2p?) without exponents.

A: The objective is to write the expression without exponents.

Q: + 1)3² – 120 000 = 2100(- how do you isolate for i?

A: Given expression is 120,000=21001+i32-1i

Q: b.) (-38/135 +65/70) (3 + 4i) 5 + 2i

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Q: arg((1+ i)(1 – i) + (-1,–1)) 7n A. + 2kn 4 " + 2kn В. 4 5n С. + 2kn 4 D. None of above

A: firstly , we will simplify the terms inside the bracket and, then we will use formula for argument…

Q: simplify(assume X>0) √(1/√81)

A: 1/sqrt(81) =1/9 or -1/9 Considering the positive square root we get, 1/sqrt(81) = 1/9 Considering…

Q: Simplify (z+1)²(3xy²)3 (9y²) 2x-³(z+1)-1

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Q: For the given numbers: Z1 = 1 – 2i, Z2 = 3 – i, Z3 = 2 – i, find: (a) Z1 · Z2 + Z3 (b) (c) |Z|

A: For the given numbers:z1=1-2i   , z2=3-i  , z3=2-iFind:

Q: Multiply each expression using the product rule: b. (4x'y*)(10x?y*). a.

A: Given : a. b6·b5b. 4x3y410x2y6

Q: 30) What is the difference when (4 – i) is subtracted from (2 + 5i)?

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Q: What is Im (i (3 + 2i) (7 +5i))?

A: Given that the complex number Imi3+2i7+5i   .

Q: Simplify the following:  (a.)  i11 (b.) i105 (c.) (5/i) + (2/i3) - (20/i18) (d.) (4i)3 - 4i3

A: we are given some complex equations , we have to simplify them. As per the guidelines we can solve…

Q: (b) (2 + 3i)¹+i

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Q: Simplify the expression: 4 (3z*y*)* . 2(z³)® 4,3

A: We have to simplify the given expression.