Illustration 3.6 Express each one of t standard form a + ib. 5+4i (+)²

Q: Write each of the following in standard form.(a) (1 + 4i ) / (5 - 12i )(b) ( 2 - 3i ) / (4 - 3i)

A: a) Given that,  1+4i5-12i Simplification: 1+4i5-12i=1+4i5-12i×5+12i5+12i                Rationalize…

Q: 1. Express the sum of (2 - 3i) and (6 + 4i) divided by the sum of (4 + i) and (-5- 2i) in a + bi…

A: 1)  To find the value of           {(2-3i)+(6+4i)} / {(4+i)+(-5-2i)}

Q: Show by contraposition that : Vx ERx?-7x-820 - x2 8 or x S-1

A: In this method, we prove negation of antecedent and get contradicted and get our required results.

Q: V-25+ 2iº5+3(i6)' + |9 + 8i| – 4(5+ 6i) v-36

A:

Q: Example 4.8.2 Simplify the following expressions: (a) Cov(8X +3,5Y – 2), (b) Cov(10X - 5, -3X + 15),…

A:

Q: 1+3i 5. Evaluate 1-41

A:

Q: 5 – 2i 1+i If A = find A. 2 – i -2 – 5i ? ? A = А ? ?

A: We will find out the required value.

Q: Express the following complex number in exponential form: (47.3 – 10.91)

A: Any complex number, z=x+yi can be represented in the exponential form as z=reiθ , where, r=x2+y2 and…

Q: Find the value of q such that (3 + 4i)(1 + 2i) (1 + 3i) = q(1 + i).

A: We have to simplify left hand side expression then compare both side to find the value of q.

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

A: Rationalise i^2=-1

Q: Find the following product and write the result in standard form, a + b i. (-9+4i)(6+ i)

A:

Q: 22) -2 +4i -10-6i

A:

Q: 1 Evaluate dx 2 x*V1+x 2.

A: We have to evaluate , ∫1x2 1 + x2 dx

Q: 4+ 3i 3 — 5і (b) 2+ 3i 2 – 3i

A:

Q: Simplify completely: 22+5 3z +. z十1 z-2

A:

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

A: Here we use that i=exp (πi/2).

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: 7. Simplify 188 – 3/27

A: Solution :-

Q: m(x)= 14x-1 3 서 2

A: Given : m(x)=4x-132 To find : Find the inverse and prove it by composition.

Q: 1. Simplify the following list of complex expressions to the form a + ib where a, b are real…

A: we need to simplify the given complex expression to the form a+ib we know i=-1,  i2 = -1,  i3=-i, i4…

Q: or the following quadratic function defined, (a) use the vertex formula to find the coordinates of…

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Q: 1 - 3i З 1 + 2i

A: To simplify the following expression.

Q: Find the value of a such that (3 + 4i)(1+2i) (1 + 3i) 9 = = = q(1 + i).

A:

Q: When 3+4i / 2+i is expressed in the form a + bi, what is the value of a?

A:

Q: 21 = 106 55 104 102 ܐ

A: We have to find the sum of the series.

Q: Question 10 Fimplify: 2i ( i- 1) A -2- 2i B) i c) -2i D 2- 2i

A: We want to simplify 2i(i-1)

Q: -1+5i -i

A: topic- complex numbers  real part is added and subtracted with real part and imaginary part is added…

Q: (a) Simplify i*+1 in real and imaginary parts.

A: As there are two questions given ,i only do the first.