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if cos (1-i) = a+ib, where a , b in R a...

if cos (1-i) = a+ib, where a , b `in ` R and `i = sqrt(-1)` , then

A

`a = (1)/(2)(e-(1)/(e))cos 1, b = (1)/(2)(e+(1)/(e))sin 1 `

B

`a=(1)/(2)(e+(1)/(e))cos 1,b=(1)/(2)(e-(1)/(e))sin 1`

C

`a=(1)/(2)(e+(1)/(e))cos 1,b=(1)/(2)(e+(1)/(e))sin 1`

D

`a=(1)/(2)(e-(1)/(e))cos 1,b=(1)/(2)(e-(1)/(e))sin 1`

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • Let z= a+ ib (where a,b,in R and i = sqrt(-1) such that |2z+3i| = |z^(2) identify the correct statement(s)?

    A
    `|z|_("maximum")` is equal to `3`
    B
    `|z|_("maximum")` is equal to `1`
    C
    If `|z|_("maximum")` when `z=alpha + ibeta (alpha,beta in R and I = sqrt (-1) then (alpha^(3)+beta^(3))` is equal to `27`
    D
    If `|z|_("maximum") "when" z= x+ iy (x,y in R "and" i = sqrt(-1) "then" (x^(2) +2y^(2))` is equal to 2

  • Consider the two complex numbers z and w, such that w=(z-1)/(z+2)=a+ib, " where " a,b in R " and " i=sqrt(-1). Which of the following is the value of -(b)/(a) , whenever it exists?

    A
    `3tan(theta/2)`
    B
    `1/3tan(theta/2)`
    C
    `-(1)/(3)cot theta`
    D
    `3cot""theta/2`

  • Consider the two complex numbers z and w, such that w=(z-1)/(z+2)=a+ib, " where " a,b in R " and " i=sqrt(-1). Which of the following equals to abs(z) ?

    A
    `abs(w)`
    B
    `(a+1)^(2)+b^(2)`
    C
    `a^(2)+(b+2)^(2)`
    D
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