Question #e8f6b

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Answer 1 · 2018-02-07T21:32:58

#6.4# (nearest tenth)

the two parts of the complex number are graphed on different axes.

#5# is the real part of the number, while #-4i# is the imaginary part.

#5# is graphed as #5# to the right, on the real axis.

#-4i# is graphed as #4# down, on the imaginary axis.

the modulus is the point's distance from #0#. (in the picture, the distance is shown by a thin grey line)

the value of the modulus (i.e. the length of the line) can be calculated using Pythagoras' theorem, where the modulus is the hypotenuse.

#a^2 + b^2 = c^2#

#a# and #b# are the distances from the real and imaginary axes. here, these are #5# and #4#.

#5^2 + 4^2 = c^2#

#c^2 = 25 + 16 = 41#

#c = sqrt41#

this means that the length of the line, and therefore the value of the modulus, is #sqrt41# as an exact value.

rounded, it is #6.4# to the nearest tenth.