1) Write the following complex numbers in the standard form, then find their imaginary part, modulus, argument and complex conjugate. 2 1 Z1 = (3 – i)(1+ 2i) Z2 = (1 – 3i)(2 + i)’ 1 3 23 = 2+i 2 i 2i -

Q: Let i denote the square root of-1. For the two complex numbers z = 3e and w = 6e find z. w. Give…

A:

Q: Find the product of the two complex numbers. 21 = 3 (cos 10 +i sin 10") and zg=-2(cos 35" +i sin…

A: Given: x1=3(cos 10°+i sin10°) and x2=-2(cos 35°+i sin 35°)

Q: 4. Find the modulus, Iz], and argument, 0 , of the complex number. -1 + i

A:

Q: 8. Consider the complex number z = 5+8i and w = 3– 3i. Write down the real and imaginary parts of…

A: Proceed as shown

Q: Represent the complex number geometrically.(1 + 2i)2

A: Represent the complex number geometrically.(1 + 2i)2

Q: Given the two complex numbers: 2₁ = 2 + 4i and Z₂ = √5 -3i 1) Find the value of the complex number…

A:

Q: (a) If z is a complex number such that z =8i, write z in the form a +bi. Given that =, =2 b where a…

A: These are complicated & lengthy problems,so I can do it in Advanced mathematics.

Q: Represent the complex number geometrically.2i(2 + 3i)

A: given 2i(2+3i) =4i-6=-6+4i It is represented in a complex plane. where x-axis represents real value…

Q: 1. Determine the two square roots of the given complex numbers in Cartesian form and show the…

A:

Q: Use De Moivre’s theorem to change the given complex number to the form a + bi, where a and b are…

A: Given: Let z=-1+i8  To Find: To change the given complex number into a+ib form using De Moivre’s…

Q: Given the two complex numbers: z1 = 6(cos π/2 + i sin π/2) and z2= 3/2(cos π/4 + i sin π/4) Find the…

A: we have to find

Q: How may the following complex numbers be obtained fromz = x + iy geometrically? Sketch. 1 / z

A:

Q: Find the modulus and argument of the complex number (2+i/3-i)2. Also express -5+ 5i in polar form

A: 2+i3-i2=2+i3-i·3+i3+i2=6+2i+3i+i29-i22=6+5i+-19--12=5+5i102=25+50i+25i2100=25+50i+25-1100=50i100=i2=…

Q: Two complex numbers z1 and z2 are given by z1 = 3 + 2i and z2 = − 1 − 4i. Evaluate, (a) |z1z2| (b)…

A:

Q: 3. How may the following complex numbers be obtained from z = x + iy geometrically? Sketch. а. 2 b.…

A:

Q: Find all complex numbers z satisfying z³ = 27i and give your answer as a comma-separated list of…

A: We have to find Z value

Q: 2.1 Find the value of x and y from the given complex equation (-2+ i)x + 2y =1+ 3i. 2.2 Write the…

A:

Q: Find the argument of the complex number 3/3 – 3i in the interval 0 <0< 2. Express your answer in…

A:

Q: 2 – i Find the conjugate of the complex number in the form of a + bi. 1– 2i

A:

Q: Find the quotient z1/z2 of the complex numbers.Leave answers in polar form.Express the argument as…

A: Given : two complex numbers as  z1=20cos75°+isin75°z2=4cos25°+isin25° To find : The quotient z1z2.…

Q: Find all complex numbers z satisfying z4 = -8+8 \3i and give your answer as a comma-separated list…

A:

Q: The complex number Z1and Zzare given by, Z1 = 3 – 5i and Z, = -1+4i Determine: 221 + 5Z2 O1+ 10i 01-…

A: Given: Z1=3-5i &amp; Z2=-1+4i We know that; a+bi±c+di=a±c+b±di And ca+bi=ca+cbi, where c is scalar.

Q: Show that if z1 and z2 are complex numbers, then zi + z2 = Zī + Z2.

A: Suppose the two complex numbers are z1 and z2 such that where a,c are real parts and b,d are…

Q: Find the conjugate, argument and modulus of the complex number Z=1+i3

A:

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: Use De Moivre’s theorem to change the given complex number to the form a + bi, where a and b are…

A: 1-i10 Consider, z=1-i Now, z=12+-12=2 &amp; θ=tan-1yx=tan-1-11=2π-tan-11     ∵The complex number 1-i…

Q: 3. Determine all complex numbers z for which |2z – 1| < 2|2 – i|.

A: The given problem is to find all the complex numbers that satisfies the given complex inequality.

Q: 1. Write the complex number i+ in the form of reie.

A:

Q: How may the following complex numbers be obtained fromz = x + iy geometrically? Sketch. -z

A:

Q: B. Express in the form of a complex number x+iy 1. (2+34)+(-4+5i) 2. (3+ 2i)(3 – 31) 8+4i 3. 1-i

A:

Q: Write the standard form of the complex number. (Round numerical values to four decimal places.)…

A:

Q: 8. Consider the complex number z = 2 + i and w = 7 – 2i. Write down the real and imaginary parts of…

A: Given : The complex numbers z = 2 + i  and w  = 7 - 2i.   To write the real and imaginary parts of…

Q: What is the algebraic form of the complex number 13 e 12+5i 5-12i 12-5i 5+12i

A: We will use the basic theory of complex numbers to answer this question.

Q: Use De Moivre’s theorem to change the given complex number to the form a + bi, where a and b are…

A: 3+3i5 Consider, z=3+3i Now, z=32+32=32&amp;θ=tan-1yx=tan-133=tan-11=π4 Now trigonometric form is,…

Q: The complex number Z1 and Z2 are given by, Z1 = 3 - 5i and Z2 = -1+4i %3D Determine: 2Z1 +5Z2

A: topic - complex numbers

Q: Find the quotient z1/z2 of the complex numbers.Leave answers in polar form.Express the argument as…

A: r(cos x + i sin x)= r eix

Q: Solve the following complex numbers: Z1 = 5+3i; Z2 = 4+5i ; Z3 = 3-i 1. The product of Z1*Z2 2. The…

A:

Q: Evaluate the complex number: (cos 20+i sin 20)² (cos 30 + i sin 30)2 (cos 40 + i sin 40) (cos 60 +i…

A:

Q: 1. Write the complex number 2+ iv3 in the form of reio . (2 Marks)

A: Here we first find modulus and arg then convert this into polar form

Q: (b) Find the conjugate and modulus of the following complex number Z = /5+ i6

A: Given complex number is z=5-i6 Since, conjugate of a complex number a+ib is a-ib Hence, conjugate of…

Q: 7. Write down complex numbers in the trigonometric and expone forms a) z = 16i; b) z = –1; c) z =…

A:

Q: 11 (6i – 9) = Your answer should be a Complex number in the form a + bi where a and b are real…

A: Complex number multiply

Q: Simplify the complex number z = j(-1+ j) and plot the result on your Argand diagram. Then, find the…

A: Given :           z = j(-1 + j)        To simplify z and to plot the result on Argand diagram.…

Q: Express the given complex number in rectangular form. Express components in exact form. (No decimal…

A: Given query is to find rectangular form.

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…

A:

Q: Find the quotient z1/z2 of the complex numbers. Leave the answer in polar form with the argument…

A:

Q: Given the complex numbers z1 = 5 (cos(139°) + i sin(139°)) and z2 = 2 (cos(-94°) + i sin(-94°)),…

A:

Q: If the complex number z and its conjugate z' satisfy zz' + 2(z - z') = 12 + 8i, then the values of z…

A: Explanation of the answer is as follows