Suppose z is a complex number that possesses a fourth root w that is neither real nor pure imaginary. Explain why the remaining fourth roots are neither real nor pure imaginary

Q: Find the 5™ roots of the complex number [(2+x) – 5i] , where x = last digit of your ID Number.

A: To find- Find the 5th roots of the complex number 2 + x - 5i, where x = 2

Q: #4. Show that equation | 2-1-2|=1 Can be written as 121²2 Re Z-2 Im Z +1=0.

A: Given equation  z-1-i  =1. Show that: z2 -2 Rez -2 Imz +1=0.

Q: Q2\ If z = 1 + i, what is z3 + z? + z + 1 as a single complex number?

A: Use the following formulae, to simplify the given expression.…

Q: If a complex number z satisfies z = z-1, what can be said about the number? Are con Nay/ Say that…

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Q: Let Find formulas for the entries of M", where n is a positive integer. (Your formulas should not…

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Q: Ifz₁, Z2, Z3 are complex numbers such that (2/z₁)=(1/z₂)+(1/z3), then show that the points…

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Q: 2) Consider complex numbers z₁ = 4-3i and z₂ = −6+4i and compute a. Z₁ Z₂ b. 21 Zz C. Z1

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Q: #7. Find the four roots of the equation Z² +4=0 and use them to factor 24+4 into quadratic factors…

A: Answer:-

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: Let z be a complex number. Then Im(-iz+1)= * O =liz-1| O None of these Ozliz-1| Sliz-1|

A: The last option is correct.

Q: Pick two complex numbers (like a + bi and c + di) and consider if the following statement is True or…

A: Set of pure imaginary numbers

Q: True or False The polar form of a nonzero complex number is unique.

A: The polar form of a nonzero complex number is unique.

Q: #6. Find the square roots of (a) 2i; (b) 1-√3 i and express them in rectangular wordinates. #7. Find…

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Q: Find all the roots of the following complex numbers and sketch them on the Argand plane (-v3 – 1)/

A: Let  z=(-3-j)3/4 ⇒z=(-3-j)314…

Q: Let the b and c randomly chosen numbers from interval [-A,A]. Determine the probability that the…

A: It is given that  and  are randomly chosen number on the interval The quadratic equation is

Q: Z₁ = (1+i)² 2 (1 - i)² 3 I

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Q: Find the indicated roots and graph them in a complex plane URGENT PLEASE

A: First we have to convert given complex number into polar form-

Q: 2z - 8| 0 | ² + |z + i|² < 2. ≥ 1, show that 1+z+z²+

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Q: If 4,,2 are two complex numbers then : ollz|-|z||>|z1-z |z,+z2ls\z]\+|z3l |

A: If z1,z2 are two complex numbers, then (a) z1+z2=z1+z2 (b) z1-z2&gt;z1-z2 (c) z1+z2≤z1+z2 (d)…

Q: Let 2₁, 22, 23 be three complex numbers and a, b, c be real numbers not all zero, such that a+b+c=0…

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Q: 7. Express the complex number 1/(1+ jV3) in the form Aejº

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Q: Present complex number z in algebraic form =* + 23D 35 1-3i

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Q: The set of all complex number z in the complex plane satisfying Im(z^2)=2 is a a. straight line b.…

A: The set of all complex numbers z in the complex plane is satisfying

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: If a complex number z satisfies z2* = 2-1, what can be said about the number? if the fonrepleziott å…

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