If z = x + yi is a complex number, then |z| equals which of the following? (a) x? + y2 (c) Vx + y (b) |x| + |y| (d) V]x| + |y|

Q: (a) 2122 + 22Z3 + 2321 (b) (c) Re(z) +Im(2?

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

Q: Find each of the following. a = 2i +j b = i - 4j (a) a + b 3 i+ -3 (b) 4a + 5b X i+ -15 |× j 6. (c)…

A: A detailed solution is given below.

Q: Suppose the complex numbers x and y satisfy the following equations: xy - y² xy + 2x² = = 3 1 (A) 8…

A: Answer is D. 16

Q: If z = 1+ 2i and w = 3+ 4i, express the following in the rectangular form: (a) 2|w| +(1 – i)2² w + z…

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Q: Find all (real or complex) numbers z1 and z2 such that Z1+zz=2+4i Z1z2=-10–20i

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Q: Find the value of q such that (3 + 4i)(1 + 2i) (1 + 3i) = q(1 + i).

A: We have to simplify left hand side expression then compare both side to find the value of q.

Q: 3. Show that (1+i) = 2i

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Q: 4+ 3i 3 — 5і (b) 2+ 3i 2 – 3i

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Q: Which of the following expressions simplify to 4x? y? (4xy) (4x) (&xy²) (2r°yz) y(2x²y)

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Q: Find all values of the following roots. a) (31)¹/2 b) (-i)¹/4 c) (-1)¹/4

A: According to guidelines we can solve only first three subparts, please repost remaining subparts.

Q: Ax + Bx (x- 1)(x + 1) Given that can be expressed in the form 2 + find the values of 2(x - 1) 2(x +…

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

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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: solve 5cos (2θ) = -3 over the reals

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Q: Express −i+j in the form [a,b]

A: Simplification

Q: 1. What are the roots of the equation (x + 1)(4x – 3) = 0? C) x= 1, - D) x= 1 A) x = -1,3 B) x= -1,

A: (x+1)(4x-3)=0⇒(x+1)=0 or (4x-3)=0⇒x=-1 or 4x=3⇒x=-1 or x=34⇒x=-1 ,34