Question 9 What is the exponential form of the complex number 4 + 3i A) 5 e 153,130 B) 5 e 136,870 C) 7e i53,130 D) 7e 36,87o

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: 1. Consider the nonzero complex numbers 21 5i z2 = 4i and z3 (z1 + z2 + 23) (a) Evaluate (z1 22 Z3)…

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Q: a) Evaluate (1 + 4i)² in the form x + iy. +i b) Evaluate 1 + 5i - 4i7 +6i6 in the form x + iy. +i c)…

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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: In Exercises 1 through 8 use the parallelogram law to form the sum and difference of the given…

A: Solution

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: Re((1+i)z)=1 set an Argand diagram for complex number z

A: Given a complex number : z = x + iy We need to plot for the part : Re((1+i)z) = 1 in the Argand…

Q: IN! Write each complex number in standard form. 4 10. 25 Choices for 10-16: 1 A) 11. B) C) -- 49 D)…

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Q: 2. Write each of the functions in the form Aet cos Bt +iBed sin Bt, where a, B, A, and B are real…

A: To write each of the given function in the form  A* eatcos(bt)+Beat sin(bt) . We apply three…

Q: cos x if x 0 -

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Q: 11. Write the quotient of the complex numbers in the standard form z=x+ iy. 3+i 1-2i

A: If you like the solution then please give it a thumbs up.... The Answer is:           Standard form…

Q: Express e a) 0-e²i b) 0+e²i c) e² - ei c) e² +e²i in a +ib form.

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Q: 1. Solve the following equations. a) (7+2/)+(4-3) b) (5-2/ (2-)(4+2) d) 2- 1+2 e) 21-3 2. Find x in…

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Q: Write all values of a) ln(e-2)   b) ln(-3)

A: In this solution, we will find the values: (a) lne-2 and (b) ln-3. We know that lnab=blna. We know…

Q: a) Let a complex number z =-5i+3. Find in the standard form x+ yi . IN

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Q: Operate (3 + 7i) + (8 + 11i). A) -8 - 3i B) 10 + 19i (c) -11 - 8i D) 11 + 18i

A: We have to operate  (3+7i) +(8+11i)

Q: Write the following complex number in trigonometric form: - 2 + 2i

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: In Exercises 9 through 14 find the roots of the given complex number. 9. (1+iv3)A, 12. (-1-i). 13.…

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Q: 4. What is the simplification of the following comple expression (i = -1) 4+3i 1– 3i 13 9. 1 3 A) 10…

A: 4+3i1-3imultiply and divide by…

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

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Q: 4. What is the simplification of the following complex expression (i? = -1) 5-i 3+i

A: To simplify the given complex expression:- 5-i3-i

Q: 18 Given the complex number z = i, £$=:(2)" = A 1+i -i C -1 +i D -1

A: Topic : complex number

Q: 1. Write the complex number i+2 in the form of reio

A: The complex number z can be written in the form of . The value of r can be obtained from the formula…

Q: cos20 iii) modulus of complex z = 3 +- (cos0)² + i equal to a. V3 b.3 c. V2 d. 2 с.

A: Given

Q: a) Find the real and the imaginary parts of the following complex numbers b) (1 - i)eix/2 c) |ex/4…

A: let,

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: Calculate the logarithms of the following complex numbers

A: Logarithms of complex numbers

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: 2.2 Simplify the complex power (E) -2i and leave your answer in its simplest form.

A: Given that, the complex expression is 1+i1-i-2i.