Express the complex number z =1- 3i in the form of ree and deduce the following complex numbers in the form of a+bi. a) b) z'

Q: Prove the Euler's formula: e" = cos0+ jsin 0 using the definition of the complex number

A: We have to prove that ejθ=cosθ+jsinθ. We know that ex=1+x+x22!+x33!+x44!+.......... Now,…

Q: Find all the complex numbers x that satisfy the equation x5 - ix4 + 5x3-5ix2 + 6x - 6i = 0. Then…

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Q: Let a = 1+bi be a complex number, b>0, such that a is a real number. Evaluate 1+a+a² + . + a". ....

A: Given a complex number : a=1+bi where b>0 It is given that  a3 is a real number. We need to find…

Q: Find all complex numbers z satisfying 24 = -1 and give your answer as a comma-separated list of…

A: Given that the complex equation z4=-1

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: a) z5 = -32 b) z² + (i – 2)z + (3 – i) = 0 %3D ||

A: We have to find roots of given equation by De Moivre's formula.

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: Express the complex number 2 + 2√3 i in polar (trigonometric) form.

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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: present given complex number in polar form also find its (1+21) ¹2 (-2-√5i)"

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Q: Simplify the complex number a = that a= a + bi. 10 (1+1) ". That is, find values for a, b = R such

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Q: Rewrite the complex number 5(cos5.5+i sin5.5) in a+bi form

A: See the details solution below

Q: Express the complex number z = 9√3+9i in standard polar form.

A: The given complex number,    z=93+9i

Q: i7(√3-i10) (2 - i5)

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Q: 1. Write the complex number i+ in the form of reie.

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Q: Find all complex numbers z such that 2²=-12+16i, and give your answer in the form a+bi. Use the…

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Q: Solve the following complex number: 1. 2+i/1-i = i(x+iy), x=? ; y=? 2. (2+i)(3-2i) = a+ib, a=?;…

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Q: If Z₁=14+7i and Z2=3+17i, determine the imaginary part the complex number: Z₂ Give your answer to…

A: Given :Z1=14+7iZ2=3+17i

Q: Find all the roots of the given complex numbers a) z5 = -32 b) z² + (i – 2)z + (3 – i) = 0

A: To find - Find all the roots of the given complex numbers z5 = -32 z2 + i - 2z + 3 - i = 0

Q: 4i Rewrite the complex number 10e“ in a + bi form a b = II

A: We have to write the complex number 10e4i in a + bi form.

Q: complex form and COS U+ i sin o) be the polar form Idition and subtraction between two complex…

A: Topic:- complex number algebra