(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: For the complex numbers • w = 3-5 i • z = -4+7 i Enter exact value of the imaginary part of their…

A: Product of two complex numbers (a+ib)(c+id)=ac-bd+i(ad+bc)

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: 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: . Define complex variable and complex conjugate with example

A: Topic = Complex number

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: What is the argument of the complex number given by z = (1+ iv3)(1 + i)(cos(0) + isin(0)) Select…

A: We have to find argument.

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: Suppose the product z1z2 of two complex numbers is a nonzero real constant. Sho 2 kz1, where k is a…

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Q: Show that x+iy | g+ix / = 1₁ =1, where X +iy and y+ix are complex numbers.

A: Here, let evaluate x+iyy+ix Using the absolute rule ab=|a||b|: =|x+iy||y+ix|

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 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>z1-z2 (c) z1+z2≤z1+z2 (d)…

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: Write the following complex numbers in rectangular form (z = x + iy) el-i +1 el-i – 1'

A: I have divide each terms as a+ib form the rationalized