2 – 4i 2 – 4i Write 1+ 3i as a complex number. In other words, find real numbers a and b such that 1+ 3i = a + bi

Q: 1-10i Q2. If complex number z satisfies the equation: _2z – 57 = 3 – i where z denotes the complex…

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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: 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: N=-7+1li %3D

A: Given complex number Z=-7+11i

Q: 10 (-6 – 9i) = Your answer should be a complex number in the form a + bi where a and b are real…

A: Given  (-6 - 9i)

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: Find all complex square roots of 3+3/3 i. In other words, find all complex solutions of x= 3+33 i. i…

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Q: The conjugate of the complex number -4 – 3i is a) 3 – 4i b) 3 + 4i c) -4 – 3i Qd) -4+ 3i

A: A conjugate is where we change the sign in the middle.  i.e        Conjugate of a+ ib = a- ib

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: Find all complex square roots of i. In other words, find all complex solutions of x i

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Q: Completely factor P(x)=x" +2x'+ 8x + 32x- 128 into linear factors, given that - 4i is a zero. P(x) =…

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

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Q: Evaluate  3−3i / 1-4i  and express as a simplified complex number.

A: Given,           3-3i1-4i

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

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Q: 13. Find the complex number. real imaginary com 4 -7i O 4+7i 11i 4 - 7i 3i -28i 14. Multiply the…

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Q: 3+4i 2i Simplify the expression to a single complex number:

A: We can solve the Complex number expression by using the technique of Complex conjugate . In the…

Q: Find all complex fourth roots of -1+ 4i. Give your answers in a + bi form, separated by commas.…

A: To find complex forth roots of -1+4 i.

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

A: Consider the equation : z3+8i=0. Find the solutions of the given equation. z3+8i=0z3-8i3=0…

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

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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 & Z2=-1+4i We know that; a+bi±c+di=a±c+b±di And ca+bi=ca+cbi, where c is scalar.

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: Completely factor P(x)=x* +x + 4x+16x-192 into linear factors, given that -4i is a zero. P(x)= (Type…

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Q: 13i · (1 – 5i) = Your answer should be a complex number in the form a + bi where a and b are real…

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Q: Find all complex cube roots of – 4 – 2i. Give your answers in a + bi form, separated by commas.

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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: Find all complex square roots of -4i. In other words, find all complex solutions of x =-4i. i

A: Find the all complex solutions

Q: Divide Complex numbers 5 (2i +1) (Refer: use conjugate to simply the complex number) -2i + 1 2i + 1…

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Q: Find all complex cube roots of – 4 + 3i. Give your answers in a + bi form, separated by commas.

A: We’ll answer the first question since the exact one wasn’tspecified. Please submit a new question…

Q: (b) Give an example of a complex number z, other than ±1 or ±i, such that |2| = 1.

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

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Q: 5. Divide complex numbers. 10 а. 1-2i -3-6i b. 2i

A: Given:                a) 101-2i   Solution:                    Determining the conjugate of the…

Q: Find all complex numbers z so that z6 = 218 Express your solutions in the form a + bi, evaluating…

A: Given: z6=218 We have z6=236z=23 Let z=rcosθ+isinθ. Then, z to the power 6 gives…

Q: Find all the complex roots of (4 – 4i)1.

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Q: Find all complex numbers z satisfying 23= -27i and give your answer as a comma-separated list of…

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Q: The complex number a is given by a =-2 + 5i. i) Write down the complex conjugate a*. a +a* ii) Find…

A: α =-2+5i complex conjugate =-2-5i

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: Find a complex number z, where (10 + 6i) + z is a real number. i Then find the product of your…

A: A complex number is of the form a+ib ,where a and b are real numbers and i2=-1

Q: 6+5i -6-3i 2s

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

A: Consider the equation : z8-16=0 To Find the solutions of the given equation. z8-16 = 0        z8 =…

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: Find all complex numbers z such that z=-15-8i, and give your answer in the form a+bi. Use the square…

A: Follow next step

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: 1-18i Q2- The complex number zsatisfies the equation 4Z - 37 2-i Then Z = ......... .........

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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. 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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