Let z = 3 – 4i and w = -1+ 2i be in C. (a) Write z + w, zw, and in the form a + bi with a, b e R. (b) Find Re(z), Im(z), z, and |z|.

Q: (b) Show that i10 is real, even though i or 10i is not.

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Q: (b) Show that i³i is real, even though i or 3i is not.

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Q: Expand and simplify to express each equation in standard form. [2, 2, 2, 3, 3, 2] a) y = (x +5)(x +…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

Q: Find AB if A = [4 -3 3 -1 0 -2] and B = 4 Use the tools in the

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Q: . Let 21 2i and z2 = 1+v3i. (a) Express zi and z2 in mod-arg form. (b) Plot in the complex plane the…

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Q: Express 3-i/2+3i  in the form a + bi

A: Rationalise i^2=-1

Q: Find the conjugate of z = -2 – 4i, and compute zz. z = zz =

A: Given that: z=-2-4i

Q: 3. Find the positive value of real parts of the possible values of z that satisfy the equation: zz +…

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Q: A−1 in the block form.

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Q: Let a = – 4i – 5j and b – 7i + 3j. Find a - b

A: we have  a→=-4i→-5j→ and b→=-7i→+3j→

Q: Find a - b

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Q: Assume Z₁ = 2 - i and Z₂ = 1 + 3i. Find the product and quotient of z1 and 22. Z₁Z2 = Z1/Z2 =

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Q: If Z = 2 + 5i, write down the conjugate of Z. Multiply Z by its conjugate and write answer in the…

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Q: Add and simplify. (4 – 7i) + (4 – 8i)

A: While adding two complex numbers having real and imaginary parts, add the real part of one complex…

Q: Write i -1 - i in x + iy form.

A: Here we use that i=exp (πi/2).

Q: Find the real numbers x and y if (x – iy) (3 + 5i) is the conjugate of –6 – 24i.

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Q: If Z1 = 4 + 5i and Z 2 = -1 + I,  express in the form a + bi  (i) Z1 + Z2   (ii) Z1 – Z2

A: Formula used  sum of two complex number is given by  (a1+b1i)+(a2+b2i)=(a1+a2)+i(b1+b2)

Q: Please find cross product c=a x b, where a= and b =. For c=16i+0j+?k, please enter the missing k…

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Q: [2-3i 5 + 8i 3 – 7i | 9. Find (2 + 3i) A if A = -4 L-6- i 5i

A: We can solve this as follows:

Q: Find all values of z such that z5 =1 - i.

A: Given: z5=1-i, To find: All values of z.

Q: 5. a. Given z, = -7 + 6i(15+2) and z, = -2i(36-0) + 8i , find |z, + z2]. 4 b. Simplify (+ ), and…

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Q: Verify that              a.(b x c) = b.(c x a) = c. (a x b) if               a =4i – 3j +6k ,  b=…

A: Given that a→=4i-3j+6k, b→=5i+4j-3k, c→=4i+6j+3k We have to verify that a→·b→×c→=b→·c→×a→=c→·a→×b→

Q: For z=1+i find the product of z and its complex conjugate zZ

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Q: Express −i+j in the form [a,b]

A: Simplification