Show that dz Long 21-0 z3 +1 by arguing that this integral does not change if we replace C[0, 2] by C[0, r] for any r > 1, then use dz that goes the fact that 2³ +1 to 0 as r→∞. 16,f| Y ≤ ≤ max|f(z)|· length(y) to obtain an upper bound for

Q: Multiply complex numbers 3(cis122)4(cis213)

A: Given complex numbers: 3(cis122)4(cis213)

Q: What is the additive inverse of the complex number 3-7?

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Q: Express each of the folowing complex numbers in the form x + yi: (3 - 4)5 (4 + 37)

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Q: 7-i/-i divide complex number

A: Given : 7-ii

Q: 13. Use the exponential form of a complex number to write a + ib. ++) in the form

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Q: Do complex numbers have inverses under the complex additionoperation (‘additive inverses’)? Explain.

A: z = a+ib is a complex number Then additive inverse of z is = -a-ib

Q: Suppose z is a complex number that possesses a fourth root w that is neither real nor pure…

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Q: Find all the cube roots of 1 - i , i.e., (1 - i) ^1/3 .

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Q: Find a complex number so that c^2=i

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Q: #2. If 2₁ and 2₂ are two complex numbers, show that 12₁-221² + 12₁ +221² = 2 ( 1211² + 122 1²).

A: 2. Let z1 = a + bi and z2 = c + di be two complex numbers.      Then,          |z1|2 = a2 + b2…