1 answer

What is the trigonometric form of # (1-3i) #?

Question:

What is the trigonometric form of # (1-3i) #?

Answers

#sqrt10(cos(-1.25)+isin(-1.25) )#

Explanation:

Given a complex number z = x + iy , then in trig.form it is written

z = #r(costheta + isintheta)#

where #|z|=|x+iy|=r=sqrt(x^2+y^2)#

and #theta=tan^-1(y/x)#

here x = 1 and y = - 3

#rArr r=sqrt(1^2+(-3)^2)=sqrt10#

and #theta=tan^-1(-3)=-1.25" radians "#

#rArr(1-3i)=sqrt10(cos(-1.25)+isin(-1.25))#

.

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