Find the dot product of ū = U = (15î – 14î) . (8î + 12î) and -

Q: (b) Show that i10 is real, even though i or 10i is not.

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Q: Q2/ Write the complex number 5(cos+i sin) in its rectangular form and then plot it in the complex…

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Q: Find the conjugate of – 3i ( 2 + 5i ).

A: Solution

Q: A = 2i+3j+5k and B = 3i+6k, Determine the direct cosine of (AXB). %3D %3D

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Q: Find the complex roots of the equation z = 1 + i

A: We have to find the complex roots of the equation z5=1+i.

Q: Find the complex trigonometric form of Z =-2i

A: Trigonometric Question

Q: Transform to rectangular coordinates. 2. 4et - 2en 3. 5c1 + 4c2 + 5i + 2j 4.-Зer + бед +4i - 3j

A: Given: Let us determine the transformation to rectangular coordinates. 2). 4et-2en 3).5c1+4c2+5i+2j…

Q: Find the product in the complex plane. + i sin + i sin Cos

A: I

Q: Given the following three complex number: Z1=2+ j6, Z2 = 6– j3, and V = 30+ j40 V If I =V (Zl+Z2)…

A: When two complex numbers are added, then the real parts are added together and the complex parts are…

Q: r=2-cos(2theta) How do I convert this into rectangular form?

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Q: Find the product in the complex plane. i sin 6 + i sin 6 COS + i 6

A: Complex plane.

Q: Find the rectangular form of 3/2 et* i.e. the a + bi form.

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Q: Show that x+iy | g+ix / = 1₁ =1, where X +iy and y+ix are complex numbers.

A: Here, let evaluate x+iyy+ix Using the absolute rule ab=|a||b|: =|x+iy||y+ix|

Q: Find the product in the complex plane. cos + i sin CO: +i sin

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Q: Find the Real and Imaginary Part of 1+sqrt(3i) and plot it in the complex plane

A: Complex number of form z = x+yi Where, x is real part and y is imaginary part

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

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Q: | 2+4i -3 il %3D

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Graph the line and conic section. r = 8/(4 + cos u)

A: Graph the line and conic section. r = 8/(4 + cos u)

Q: Find w a + bi = z, where a and b are real numbers. %3D 60i-11

A: We have the formula x+iy=x2+y214costan-1xy2+isintan-1xy2

Q: Find the cosine of ZB. 3/3 в 3 6.

A: The given question is taken from the triangle in which we have to find the cosine angle of B so we…

Q: Use the parallelogram law to verify the triangle inequality |u + v| < Ju] + ]v[ for the given…

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Q: 5) A = 2i+3j+5k and B = 3i+6k, Determine the direct cosine of (AXB). %3D %3D

A: Finding the cross product of vector A and vector B  i×i=j×j=k×k=0, i×j=k, j×k=i, k×i=j, j×i=-k,…

Q: Divide the quaternion on the right 5 + 4i− 6j  of the quaternion 3i+j-2k

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Q: Simplify: i29 + i²1 + i2050 in form a + bi.

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Q: Find the product in the complex plane. +i in +i sin

A: Given: 3cosπ4+isinπ44cosπ4+isinπ4 for finding product, we simplify it

Q: Find the imaginary component if the nth root of  a + bi is determined for a = 9, b = 3, and n = 6.…

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Q: Find the distance d between z1 = (8+ 8i) and z2 = (-8+ 8i).

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Q: Evaluate the complex integral 033.png (2+3i az bz² zp bz +c if a = 6.08, b = 5, and c = 32. Then,…

A: Given the integral  ∫02+3iazbz2+cdz we have to evaluate this integral and if a= 6.08 , b=5 ,c =32 we…

Q: '5 - i хі+ C) y = 7+ 2i 3 +i,

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Q: Find w=a +bi = = Vz , where a and b are real numbers. %3D -60i – 11 W =

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Q: Find the cube root of Z^3=8i lying in the first quadrant of the complex plane. " i-V3 O 2i+v3 i+2/3…

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Q: Find the BxA where A=3j-i-2K and B= 5i+-3K

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Q: Find the distance d between 21 1 = (-7- 6i) and %3D z2 = (-15 – 12i). %3D

A: z1=-7-6iz2=-15-12i We can say that the co-ordinates of two points are (-7,-6) &amp; (-15,-12).…

Q: Find v-w, if v = -2i +2j v-w I (Type an exact answer, using

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Q: Find the product in the complex plane. COS + i sin + i sin

A: Given, 3cosπ4+isinπ45cosπ4+isinπ4 we know that, cosπ4=12sinπ4=12 Plug above values in the given…

Q: Find y as a function of t if 3y" + 31y = 0, y(0) = 7, y'(0) = 3. y(t) Note: This particular weBWork…

A: A differential equation with initial conditions is called the initial value problem. The solution of…

Q: d graph in complex plane the fo V3 – 10i 1 V3+5i

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Q: Calculate ( 3 + 2i)³. Give your answer in a + bi form Question Help: Video 1 Video 2

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Q: Find the imaginary component if the nth root of a + bi is determined for a = 10, b = 8, and n = 7.…

A: Imaginary component of the function

Q: Find the distance d between z1 = (-7– 6i) and 22 = (-15 – 12i). %3D

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Q: Find the complex roots of t

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Q: what is the phase in degrees (with respect to the +x axis) when dividing two complex numbers, Z1/Z2?…

A: We have to find the phase in degrees when dividing two complex numbers Z1/Z2 . Where ,…

Q: Find all complex values of e? isinhz. v. %D

A: Given: Complex value of ez=isinhz

Q: Find a value of b so that 15i - 3j and -4i + bj are orthogonal.

A: The given vectors are:                                            15i- 3j and -4i +bj;   Two vectors…

Q: find w., of ((1+ 2i) + (3 – 4i)) 7

A: Given that, 1+2i+3-4i12

Q: c) By using De Moivre's theorem, find (3/5 – 3i) in the standard form.

A: To find complex no. in standard form using De Moivre's theorem .

Q: 3i16 - 103 1+i 2i84 + i79

A: given the expression 3i16-i1032i84+i79 we know that i2=-1…