(a) If z is a complex number such that z =8i, write z in the form a +bi. Given that =, =2 b where a and b are real numbers, are com (b) and -2i 2 1+2i numbers such that z, +z, =2, find the values of a and b. Hence write z, z, in the form x+ yi where x and y are real numbers.

Q: 5(2-3i) – 4(4+6i)

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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: Simplify, then express each in complex number form “a+bi” 1) -3(4+2i) -2(5-3i) 2) (4+3i)^2 3) 11+2i…

A: Since you have asked multiple question, we will solve the first 3 question for you as per our guide…

Q: Write 1/ (3 + 4i ) in standard form a + bi; that is, find the reciprocal of 3 + 4i.

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Q: 1) Write a complex number in a standard form z = x + ly:: 2+i (2- i)(3i+ 4)(i+1)

A: The given complex number is

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

A: Rationalise i^2=-1

Q: Consider the two complex numbers 21 = -8-6i and z2 = -6 - 2i. Find 21-22 = (give you answer in the…

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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: Calculate the following complex numbers (i) (1 + 3i)(2 − 4i) (ii) 1 + 3i 2 - 4i 1+ 3i 2 - 4i 10

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Q: Find the principal value of the complex power: zº where z=1+i, a=1+i and B=1+i.

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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: Evaluate these complex numbers: (a) _2 – j] (b) 6 30° + j5 –- 3 + e45°

A: To find- Evaluate these complex numbers:  j31 + j2 - j2 6∠30° + j5 - 3 + ej45°

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 complex numbers z such that z²=-7+24i, and give your answer in the form a+bi. Use the…

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Q: If 'a'is a complex number such that z = 1. Find the value of a, so that the equation az? +z+1=0 has…

A: Explanation of the answer is as follows

Q: Find a complex number for which Arg(z bar) does not equal -Arg(z).

A: For all non zero complex number we have Arg(z bar) = - Arg (z)  as if z = x+iy  which imples z¯ = x…

Q: 5. (a) Let z = (a + ai)(b+ bv3i) where a and b are positive real numbers. Without using a…

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Q: Given two complex numbers z and w such that z = (1+ i)w + (3 –- i)w, where w is the conjugate of w.…

A: z and w are two complex numbers. Such that

Q: Given the complex numbers z = 2 + j3,zz = -1 - j2,andzg=4+j4 find; Im (高)x+x@zs)+Im(zz+z) (元)

A: Given: Complex numbers are z1=2+j3, z2=-1-j2 and z3=4+j4. To find:…

Q: a

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