a) Given u = 3+4i and v = 1 – 2i. Calculate in the form u + v a + ib. Hence, calculate the modulus and argument of u + v

Q: a) Evaluate (1 + 4i)² in the form x + iy. +i b) Evaluate 1 + 5i - 4i7 +6i6 in the form x + iy. +i c)…

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Q: Write 1/ (3 + 4i ) in standard form a + bi; that is, find the reciprocal of 3 + 4i.

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Q: 1) Write a complex number in a standard form z = x + ly:: 2+i (2- i)(3i+ 4)(i+1)

A: The given complex number is

Q: Express the product of 9i5(2i³ - 3i16) in a + bi form.

A: 9i15(2i3-3i16) =(9i15)(2i3)-(9i15)(3i16) =18i15+3 -27i(15+16) =18i18 - 27i31 Now i=√(-1) i18=-1…

Q: Use the trigonometric form of a complex number to show that z-n = 1/zn , where n is a positive…

A: To prove the given identity

Q: Re((1+i)z)=1 set an Argand diagram for complex number z

A: Given a complex number : z = x + iy We need to plot for the part : Re((1+i)z) = 1 in the Argand…

Q: (а) —3 i, (b) (3 – 5i) – (1+ 5i) + i, -3 (c) i i, %3D + ||

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Q: IN! Write each complex number in standard form. 4 10. 25 Choices for 10-16: 1 A) 11. B) C) -- 49 D)…

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Q: Let a and z be complex numbers with |a| # 1 and |2| = 1. %3D z - a āz – 1 Show that w= satisfies |w|…

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Q: Q1) Find modZ and ArgZ for the complex numbers given below: 1+i√2 1-i√2 2 2+i a) Z= b) Z= +2-i

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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: a) Show that the modulus of sum or difference of two complex numbers is always less than or equal to…

A: Use the properties of complex numbers to solve this problem as in next.

Q: Express e a) 0-e²i b) 0+e²i c) e² - ei c) e² +e²i in a +ib form.

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Q: Find the modulus and argument of the following complex number. z=(3-2j) (1+2j), giving the principal…

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Q: Let u = 10i + 2j, v=i+j, and w = i-j. Find scalars a and b such that u = av + bw. a = b =

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Q: Express the number (20CBA)16 + (ABC DE)16 + (BAAA)16 in bases 8, 10 and 16.

A: This is a problem of counting and finite math.

Q: Given two complex numbers z and w such that z = (1+ i)w + (3 –- i)w, where w is the conjugate of w.…

A: z and w are two complex numbers. Such that

Q: - 4i(10 – 7i)

A: -4i(10-7i)

Q: Calculate the logarithms of the following complex numbers

A: Logarithms of complex numbers

Q: Determine u = cis(pi/16) v = cis(5pi/16) are two of the nth roots of some complex number z.what is…

A: Given: Determine u = cis(pi/16) v = cis(5pi/16) are two of the nth roots of some complex number…

Q: The modulus of a complex number x+jy is equal to

A: The modulus of a complex number x+jy is equal to

Q: Compute the order of each element in the Quaternions, Q8. Show your work.

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Q: a

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Q: Find all of the complex third roots of i .

A: given complex number is i. we have to find all of the complex third roots.