2i (i+ 5) · (1+3i), (ii) 3+ 4i

Q: a) i. Given that 'm' and 'n' are powers of 'a', state four laws of indices ii. Explain the concept…

A: Given : m and n are power of a

Q: Find z, z, and for the pair of complex numbers using trigonometric form. Z2 Zq = - 20 + 20 i, z2 = -…

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Q: Find all complex numbers z such that z-8+6i, and give your answer in the form a+bi. Use the square…

A: Given that, z2=8+6i

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: Ihe complex number z is defined by z = a + ib, where a and b are real. The complex is denoted by z*.…

A: Given: z=a+ib, z*=a-ib

Q: b) Find all complex numbers z such that z= V-7+ 24i

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Q: 3 – 5i - Write as a complex number. In other 2+ 3i words, find real numbers a and b such that 3 – 5i…

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Q: ind all complex numbers z such that z=-3-4i, and give your answer in the form a+bi. Use the square…

A: Given: z2=-3-4ilet z = x+yi   then z2=x+yi2substituting z2=x+yi2 in z2=-3-4i…

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: A if z, and z, are complex numbers Z2 Show that ()= Z 22

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Q: If a2 1,Find all complex numbers z which satisfy the equaution z +a| z +1+i=0.

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Q: 14. A square root of a complex number w = c + di is defined to be a complex number z = a + bi that…

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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: 1 d) In this thesis we consider complex numbers and in terms of the imaginary unit.   Find all…

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

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Q: (b) Given z is the conjugate of a complex number z such that z=6+8i Find the complex number z whose…

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Q: 1-18i Q2- The complex number z satisfies the equation 4Z – 3Z* = 2-i Then Z =

A: complex number

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

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Q: 2Q Express the complex number 1+ 3i in the form x + yi, where x and y are real numbers. 1-2i

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Q: Find all complex numbers that are solutions of the given equation. Leave your answers in standard…

A: Given complex equation is: z4+8+83i=0⇒z4=-8-83i⇒z=-8-83i14 Let us consider, r cos θ=-8  ;  r sin…

Q: Find all complex numbers z such that z2=8−6i, and give your answer in the form a+bi. Use the square…

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Q: If z=3-4i then express these following complex numbers in the form of a+ib: (a) (=+1)(=+i) 2z (b)

A: If z = a + ib and w = c + id then z+w = (a+ib) + (c+id)       = (a+c) + i(b+d)

Q: Sixth roots of 64i (a) Use the formula z = 0+27tk cos +i sin 0+27tk to find the indicated roots of…

A: We have to find the sixth roots of 64i, using the expression zk=rn(cosθ+2πkn+ i sinθ+2πkn) First we…

Q: ind the roots of complex numbers 1. z3 = 2 – 3i

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Q: Write the complex number w = (−√3) - 3i in polar form and mark it in the complex plane

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Q: Applying De Moivre 's theorem in writing the complex number (-1-i)* in the form a + bi, the value of…

A: Given. We need to simply the complex number (-1-i)⁸ usi de moivres theoram. De moivers theoram…

Q: 1. (a) If z1 = -3 - 5i and z2 = -5 – 7i are the two complex numbers, then %3D 21 + 22 + i123 21 – 22…

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Q: Given that Z1 and Z2 are complex numbers, show geometrically or otherwise that |Z1| - |Z2| is less…

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Q: (a) Find all the complex roots of (7+6i)/3

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Q: (a) Find the modulus and argument of the complex number z =1+ v3i (b) Consider the complex number…

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Q: Find all complex numbers z satisfying 4 = -8-8 3i and give your answer as a comma-separated list of…

A: Solve the following

Q: A complex number z satisfies arg z = 5. (a) Use a diagram to show that |z-2i| > 1. (b) For which…

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Q: The complex numbers z1, z2, and z3 are the vertices of a triangle and satisfy the following…

A: Given:          z1-z2z2-z3=1-i32         multiply numerator and denominator with1+i3…

Q: 1. Solve the equation (z+6i°)(3i° – 5i’ ) =-8(1– 4i) for the complex number z in standard form.

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Q: If |x = 3i| <5, then prove that the complex number z also satisfies the inequality i(z+1)+1| <25.

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

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Q: Jusiti WX+wyi Solve the following example of complex numbers Winne

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Q: Let z be a complex number, find therange of real values of a for which the equation. z+alz-1+2i=0has…

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Q: 32. Evaluate (2i)' and express the result in rectangular form of complex number. A) 0.350 + 0.187i…

A: Given that (2i)i We need to express the given complex number of the form of x + iy

Q: 3. Given a complex number a + bi, the value of a is called the part. part and the value of b is…

A: Give query is to give the names of 'a' and 'b'.

Q: Find all complex numbers z such that z2=-5+12i, and give your answer in the form a+bi. Use the…

A: The complex number is z2=-5+12i

Q: 2.21 Consider the calculations of complex numbers C. (a) Let z = 2 - 3i and w = -1 + i. Determine…

A: Substitute the value of z and w in zw and multiple the complex numbers using the distributive…

Q: 5. Find all complex numbers of the form z = a + bi , where a and b are real numbers such that zz' =…

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Q: 1) Find the real and imaginary parts of the given complex numbers, sketch the position of each…

A: See the attachment

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…

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Q: Q(1): Derive formula for the product and division of two complex number.

A: Our objective is to derive formula for product and division of two complex numbers...

Q: 4. (a) What is the complex plane? How do we graph a complex number z = a + bi in the complex plane?…

A: (a) Complex plane: The complex plane is defined as a Z-plane which is established by real axis and…

Q: 1. Given two complex numbers z, = 2+i and zz =1-2i. a) Determine the value of k if -= kz, b) Express…

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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