Write the complex number 4(cos-135*+ i sin-135*) in the form a+bi.?

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A) -square root of 2- square root of 2i

B) -2square root if (2)+2square root of 2i

C) -2square root of (2)- 2square root of 2i

D) -square root(2)+ square root of (2i)

1 Answer

  • If you hold down ALT and type 0176 on the number pad on the right of the keyboard,

    you get the ° symbol.

    Is the angle + or – 135° ?

    It helps to put ( ) around the number to make it clear.

    as in sin(135°) or cos(-135°).

    If it’s +, then

    cos 135° = – sqrt(2)/2

    sin 135° = sqrt(2)/2

    so plugging those into the expression,

    we get answer (B)

    which should be written as

    -2 sqrt(2) + ( 2 sqrt(2) ) i

    to avoid confusion as what is under the square root sign.

    If the angle in question is -135°, then the sin function is also negative,

    and the answer is (C)

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